{"id":10869,"date":"2024-07-16T10:44:41","date_gmt":"2024-07-16T03:44:41","guid":{"rendered":"https:\/\/cloud.z.com\/vn\/?p=10869"},"modified":"2024-06-24T10:46:22","modified_gmt":"2024-06-24T03:46:22","slug":"domain-of-a-function","status":"publish","type":"post","link":"https:\/\/cloud.z.com\/vn\/en\/news\/domain-of-a-function\/","title":{"rendered":"Domain of a Function l\u00e0 g\u00ec? 6 ph\u01b0\u01a1ng ph\u00e1p x\u00e1c \u0111\u1ecbnh Domain of a Function"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Domain of a Function l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0a v\u00e0o h\u00e0m s\u1ed1 \u0111\u00e3 cho. N\u00f3i c\u00e1ch kh\u00e1c, n\u00f3 l\u00e0 t\u1eadp h\u1ee3p c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 thay v\u00e0o b\u1ea5t k\u1ef3 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o c\u1ee7a h\u00e0m s\u1ed1. T\u1eadp h\u1ee3p c\u00e1c gi\u00e1 tr\u1ecb y kh\u1ea3 thi c\u1ee7a h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1eadp gi\u00e1 tr\u1ecb. <\/span><span style=\"font-weight: 400;\">N\u1ebfu b\u1ea1n mu\u1ed1n bi\u1ebft c\u00e1ch t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 trong c\u00e1c tr\u01b0\u1eddng h\u1ee3p kh\u00e1c nhau, h\u00e3y theo d\u00f5i b\u00e0i vi\u1ebft b\u00ean d\u01b0\u1edbi c\u1ee7a Z.com.<\/span><\/p>\n<div class=\"tg_wrap_cbsv tg_wrap_cbsv_blue\" style=\"margin: 20px 0px; border-radius: 4px; border: 2px solid #0066b2;\"><cite style=\"margin: 0px; background-color: #0066b2; color: #fff; border-top-left-radius: 2px; border-top-right-radius: 2px; font-size: 19px; padding: 12px 20px; font-weight: bold; display: block; font-style: normal;\">B\u1ea1n \u0111ang mu\u1ed1n x\u00e2y d\u1ef1ng m\u1ed9t trang web c\u1ee7a ri\u00eang m\u00ecnh<\/cite><\/p>\n<div class=\"textwidget\" style=\"padding: 20px; background: #70c2e280;\">\u0110\u0103ng k\u00fd ngay t\u00ean mi\u1ec1n th\u01b0\u01a1ng hi\u1ec7u t\u1ea1i Tenten.vn ch\u1ec9 v\u1edbi 2 c\u00fa click chu\u1ed9t: <strong>Ki\u1ec3m tra s\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a t\u00ean mi\u1ec1n: Nh\u1eadp t\u00ean mi\u1ec1n v\u00e0 nh\u1ea5n \"ki\u1ec3m tra\".<\/strong> <span style=\"color: #ffff00;\"><a class=\"btn_combi_sv\" style=\"font-weight: bold; color: #ffff00; padding: 8px 26px 8px 26px; font-size: 20px; line-height: 30px; border-radius: 56px; text-shadow: none; background: #0066b2; display: table; margin: 0px auto;\" href=\"https:\/\/tenten.vn\/vi\/bang-gia-ten-mien?code=knjcpEfWoTSzUNMw&amp;idCampaign=3080\">B\u1ea2NG GI\u00c1 T\u00caN MI\u1ec0N M\u1edaI NH\u1ea4T<\/a><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/bit.ly\/3QYbaqa\">V\u00e0o nh\u00f3m Zalo nh\u1eadn \u01b0u \u0111\u00e3i t\u00ean mi\u1ec1n t\u1ea1i \u0111\u00e2y<\/a><\/li>\n<li>Hotline: (024) 71 089 999<\/li>\n<li>Email: info@tenten.vn<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h2><b>Nh\u1eefng \u0111i\u1ec1u b\u1ea1n c\u1ea7n bi\u1ebft<\/b><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1: L\u00e0 t\u1eadp h\u1ee3p c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o (x) m\u00e0 khi \u0111\u01b0a v\u00e0o h\u00e0m s\u1ed1 s\u1ebd cho ra m\u1ed9t gi\u00e1 tr\u1ecb \u0111\u1ea7u ra (y).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">X\u00e1c \u0111\u1ecbnh t\u1eadp x\u00e1c \u0111\u1ecbnh: T\u00f9y thu\u1ed9c v\u00e0o nhi\u1ec1u y\u1ebfu t\u1ed1 nh\u01b0: c\u00f3 bi\u1ebfn s\u1ed1 xu\u1ea5t hi\u1ec7n \u1edf m\u1eabu s\u1ed1 ho\u1eb7c n\u1eb1m trong d\u1ea5u c\u0103n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">K\u00fd hi\u1ec7u t\u1eadp x\u00e1c \u0111\u1ecbnh: D\u00f9ng hai \u0111i\u1ec3m \u0111\u1ea7u cu\u1ed1i, ng\u0103n c\u00e1ch b\u1eb1ng d\u1ea5u ph\u1ea9y. S\u1eed d\u1ee5ng ngo\u1eb7c vu\u00f4ng n\u1ebfu \u0111i\u1ec3m n\u1eb1m trong t\u1eadp x\u00e1c \u0111\u1ecbnh, ngo\u1eb7c tr\u00f2n n\u1ebfu \u0111i\u1ec3m kh\u00f4ng n\u1eb1m trong t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/span><\/li>\n<\/ul>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 1: H\u1ecdc nh\u1eefng \u0111i\u1ec1u c\u01a1 b\u1ea3n v\u1ec1 Domain of a Function<\/b><\/h2>\n<h3><b>1. Hi\u1ec3u v\u1ec1 t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">T\u1eadp x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 t\u1eadp h\u1ee3p c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o m\u00e0 khi \u0111\u01b0a v\u00e0o h\u00e0m s\u1ed1 s\u1ebd cho ra m\u1ed9t gi\u00e1 tr\u1ecb \u0111\u1ea7u ra. N\u00f3i c\u00e1ch kh\u00e1c, t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x c\u00f3 th\u1ec3 \u0111\u01b0a v\u00e0o m\u1ed9t h\u00e0m \u0111\u1ec3 cho ra m\u1ed9t gi\u00e1 tr\u1ecb y.<\/span><\/p>\n<h3><b>2. H\u1ecdc c\u00e1ch t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a c\u00e1c lo\u1ea1i h\u00e0m kh\u00e1c nhau<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Lo\u1ea1i h\u00e0m s\u1ebd quy\u1ebft \u0111\u1ecbnh ph\u01b0\u01a1ng ph\u00e1p t\u1ed1t nh\u1ea5t \u0111\u1ec3 t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 nh\u1eefng \u0111i\u1ec1u c\u01a1 b\u1ea3n b\u1ea1n c\u1ea7n bi\u1ebft v\u1ec1 t\u1eebng lo\u1ea1i h\u00e0m, chi ti\u1ebft s\u1ebd \u0111\u01b0\u1ee3c gi\u1ea3i th\u00edch \u1edf ph\u1ea7n ti\u1ebfp theo:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">H\u00e0m \u0111a th\u1ee9c kh\u00f4ng c\u00f3 ch\u1ee9a c\u0103n th\u1ee9c ho\u1eb7c bi\u1ebfn s\u1ed1 \u1edf m\u1eabu s\u1ed1: \u0110\u1ed1i v\u1edbi lo\u1ea1i h\u00e0m n\u00e0y, t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">H\u00e0m c\u00f3 d\u1ea1ng ph\u00e2n th\u1ee9c v\u1edbi bi\u1ebfn s\u1ed1 \u1edf m\u1eabu s\u1ed1: \u0110\u1ec3 t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a lo\u1ea1i h\u00e0m n\u00e0y, b\u1ea1n c\u1ea7n \u0111\u1eb7t m\u1eabu s\u1ed1 b\u1eb1ng 0 v\u00e0 lo\u1ea1i tr\u1eeb gi\u00e1 tr\u1ecb x t\u00ecm \u0111\u01b0\u1ee3c khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">H\u00e0m c\u00f3 bi\u1ebfn s\u1ed1 n\u1eb1m trong d\u1ea5u c\u0103n: \u0110\u1ec3 t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a lo\u1ea1i h\u00e0m n\u00e0y, b\u1ea1n ch\u1ec9 c\u1ea7n \u0111\u1eb7t bi\u1ec3u th\u1ee9c b\u00ean trong d\u1ea5u c\u0103n l\u1edbn h\u01a1n 0 (&gt; 0) v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">H\u00e0m s\u1eed d\u1ee5ng logarit t\u1ef1 nhi\u00ean (ln): Ch\u1ec9 c\u1ea7n \u0111\u1eb7t bi\u1ec3u th\u1ee9c trong ngo\u1eb7c l\u1edbn h\u01a1n 0 (&gt; 0) v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0110\u1ed3 th\u1ecb: Ki\u1ec3m tra \u0111\u1ed3 th\u1ecb \u0111\u1ec3 xem gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a x ho\u1ea1t \u0111\u1ed9ng.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Quan h\u1ec7: \u0110\u00e2y s\u1ebd l\u00e0 m\u1ed9t danh s\u00e1ch c\u00e1c t\u1ecda \u0111\u1ed9 x v\u00e0 y. T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a b\u1ea1n \u0111\u01a1n gi\u1ea3n l\u00e0 danh s\u00e1ch c\u00e1c t\u1ecda \u0111\u1ed9 x.<\/span><\/li>\n<\/ul>\n<div id=\"attachment_24281\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img aria-describedby=\"caption-attachment-24281\" loading=\"lazy\" class=\"size-full wp-image-24281\" src=\"https:\/\/www.hostify.vn\/blog\/wp-content\/uploads\/2024\/06\/domain-of-a-function-2.png\" alt=\"H\u1ecdc nh\u1eefng \u0111i\u1ec1u c\u01a1 b\u1ea3n v\u1ec1 Domain of a Function\" width=\"800\" height=\"600\" \/><p id=\"caption-attachment-24281\" class=\"wp-caption-text\">H\u1ecdc nh\u1eefng \u0111i\u1ec1u c\u01a1 b\u1ea3n v\u1ec1 Domain of a Function<\/p><\/div>\n<h3><b>3. Bi\u1ec3u di\u1ec5n ch\u00ednh x\u00e1c t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00e1ch vi\u1ebft t\u1eadp x\u00e1c \u0111\u1ecbnh tuy \u0111\u01a1n gi\u1ea3n nh\u01b0ng c\u1ea7n ch\u00ednh x\u00e1c \u0111\u1ec3 th\u1ec3 hi\u1ec7n c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m cao trong b\u00e0i t\u1eadp v\u00e0 b\u00e0i ki\u1ec3m tra. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t v\u00e0i \u0111i\u1ec1u b\u1ea1n c\u1ea7n bi\u1ebft v\u1ec1 c\u00e1ch vi\u1ebft t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a m\u1ed9t h\u00e0m:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0110\u1ecbnh d\u1ea1ng: K\u00fd hi\u1ec7u t\u1eadp x\u00e1c \u0111\u1ecbnh g\u1ed3m m\u1ed9t d\u1ea5u ngo\u1eb7c vu\u00f4ng ho\u1eb7c tr\u00f2n m\u1edf \u1edf ph\u00eda tr\u01b0\u1edbc, ti\u1ebfp theo l\u00e0 2 gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0 cu\u1ed1i c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c ng\u0103n c\u00e1ch b\u1eb1ng d\u1ea5u ph\u1ea9y, cu\u1ed1i c\u00f9ng l\u00e0 d\u1ea5u ngo\u1eb7c vu\u00f4ng ho\u1eb7c tr\u00f2n \u0111\u00f3ng.[1]<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: [-1,5). \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a r\u1eb1ng t\u1eadp x\u00e1c \u0111\u1ecbnh b\u1eaft \u0111\u1ea7u t\u1eeb -1 \u0111\u1ebfn 5.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">D\u1ea5u ngo\u1eb7c vu\u00f4ng [ v\u00e0 ]: Th\u1ec3 hi\u1ec7n gi\u00e1 tr\u1ecb n\u1eb1m trong t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Trong v\u00ed d\u1ee5 tr\u00ean, [-1,5), t\u1eadp x\u00e1c \u0111\u1ecbnh bao g\u1ed3m -1.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">D\u1ea5u ngo\u1eb7c tr\u00f2n ( v\u00e0 ): Th\u1ec3 hi\u1ec7n gi\u00e1 tr\u1ecb kh\u00f4ng n\u1eb1m trong t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Trong v\u00ed d\u1ee5 tr\u00ean, [-1,5), s\u1ed1 5 kh\u00f4ng n\u1eb1m trong t\u1eadp x\u00e1c \u0111\u1ecbnh. T\u1eadp x\u00e1c \u0111\u1ecbnh d\u1eebng l\u1ea1i ngay tr\u01b0\u1edbc 5, ngh\u0129a l\u00e0 \u0111\u1ebfn 4.999\u2026<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">K\u00fd hi\u1ec7u \u201cU\u201d (li\u00ean h\u1ee3p): \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 k\u1ebft n\u1ed1i c\u00e1c ph\u1ea7n r\u1eddi r\u1ea1c c\u1ee7a t\u1eadp x\u00e1c \u0111\u1ecbnh.<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: [-1,5) U (5,10]. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a r\u1eb1ng t\u1eadp x\u00e1c \u0111\u1ecbnh b\u1eaft \u0111\u1ea7u t\u1eeb -1 \u0111\u1ebfn 10 (bao g\u1ed3m c\u1ea3 10), nh\u01b0ng c\u00f3 m\u1ed9t kho\u1ea3ng tr\u1ed1ng t\u1ea1i gi\u00e1 tr\u1ecb 5. \u0110\u00e2y c\u00f3 th\u1ec3 l\u00e0 k\u1ebft qu\u1ea3 c\u1ee7a m\u1ed9t h\u00e0m c\u00f3 bi\u1ec3u th\u1ee9c \u201cx - 5\u201d \u1edf m\u1eabu s\u1ed1.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">B\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng nhi\u1ec1u k\u00fd hi\u1ec7u \"U\" n\u1ebfu t\u1eadp x\u00e1c \u0111\u1ecbnh c\u00f3 nhi\u1ec1u kho\u1ea3ng tr\u1ed1ng.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">K\u00fd hi\u1ec7u v\u00f4 c\u1ef1c v\u00e0 \u00e2m v\u00f4 c\u1ef1c: Th\u1ec3 hi\u1ec7n t\u1eadp x\u00e1c \u0111\u1ecbnh m\u1edf r\u1ed9ng v\u00f4 h\u1ea1n theo m\u1ed9t h\u01b0\u1edbng nh\u1ea5t \u0111\u1ecbnh.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Lu\u00f4n s\u1eed d\u1ee5ng d\u1ea5u ngo\u1eb7c tr\u00f2n ( ) v\u1edbi k\u00fd hi\u1ec7u v\u00f4 c\u1ef1c, kh\u00f4ng d\u00f9ng d\u1ea5u ngo\u1eb7c vu\u00f4ng [ ].<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">L\u01b0u \u00fd r\u1eb1ng c\u00e1ch k\u00fd hi\u1ec7u n\u00e0y c\u00f3 th\u1ec3 kh\u00e1c nhau t\u00f9y thu\u1ed9c v\u00e0o v\u00f9ng mi\u1ec1n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">C\u00e1c quy t\u1eafc n\u00eau tr\u00ean \u00e1p d\u1ee5ng cho Anh v\u00e0 Hoa K\u1ef3.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 v\u00f9ng s\u1eed d\u1ee5ng m\u0169i t\u00ean thay v\u00ec k\u00fd hi\u1ec7u v\u00f4 c\u1ef1c \u0111\u1ec3 th\u1ec3 hi\u1ec7n t\u1eadp x\u00e1c \u0111\u1ecbnh m\u1edf r\u1ed9ng v\u00f4 h\u1ea1n theo m\u1ed9t h\u01b0\u1edbng.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">C\u00e1ch s\u1eed d\u1ee5ng d\u1ea5u ngo\u1eb7c c\u0169ng r\u1ea5t kh\u00e1c nhau gi\u1eefa c\u00e1c v\u00f9ng. V\u00ed d\u1ee5, B\u1ec9 s\u1eed d\u1ee5ng d\u1ea5u ngo\u1eb7c vu\u00f4ng ng\u01b0\u1ee3c thay v\u00ec d\u1ea5u ngo\u1eb7c tr\u00f2n.<\/span><\/li>\n<\/ul>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 2 trong 6:\u00a0<\/b><\/h2>\n<h3><b>1. Vi\u1ebft b\u00e0i to\u00e1n<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3 s\u1eed b\u1ea1n \u0111ang gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">f(x) = 2x \/ (x^2 - 4)<\/span><\/p>\n<h3><b>2. \u0110\u1eb7t m\u1eabu s\u1ed1 b\u1eb1ng 0 \u0111\u1ed1i v\u1edbi c\u00e1c ph\u00e2n th\u1ee9c c\u00f3 bi\u1ebfn s\u1ed1 \u1edf m\u1eabu s\u1ed1<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Khi t\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a m\u1ed9t h\u00e0m ph\u00e2n th\u1ee9c, b\u1ea1n c\u1ea7n lo\u1ea1i tr\u1eeb t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb x khi\u1ebfn m\u1eabu s\u1ed1 b\u1eb1ng 0, v\u00ec b\u1ea1n kh\u00f4ng th\u1ec3 chia cho 0. V\u00ec v\u1eady, h\u00e3y vi\u1ebft m\u1eabu s\u1ed1 th\u00e0nh m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 \u0111\u1eb7t n\u00f3 b\u1eb1ng 0.[2] Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">f(x) = 2x \/ (x^2 - 4)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x^2 - 4 = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(x - 2) (x + 2) = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x \u2260 (2, -2)<\/span><\/p>\n<h3><b>3. Bi\u1ec3u di\u1ec5n t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x = T\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c tr\u1eeb 2 v\u00e0 -2<\/span><\/p>\n<div id=\"attachment_24280\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img aria-describedby=\"caption-attachment-24280\" loading=\"lazy\" class=\"size-full wp-image-24280\" src=\"https:\/\/www.hostify.vn\/blog\/wp-content\/uploads\/2024\/06\/domain-of-a-function-1.png\" alt=\"T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m c\u00f3 ch\u1ee9a ph\u00e2n th\u1ee9c\" width=\"800\" height=\"600\" \/><p id=\"caption-attachment-24280\" class=\"wp-caption-text\">T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m c\u00f3 ch\u1ee9a ph\u00e2n th\u1ee9c<\/p><\/div>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 3: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m c\u00f3 ch\u1ee9a c\u0103n b\u1eadc hai<\/b><\/h2>\n<h3><b>1. Vi\u1ebft b\u00e0i to\u00e1n: Gi\u1ea3 s\u1eed b\u1ea1n \u0111ang gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n sau<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Y = \u221a(x - 7)<\/span><\/p>\n<h3><b>2. \u0110\u1eb7t bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">B\u1ea1n kh\u00f4ng th\u1ec3 l\u1ea5y c\u0103n b\u1eadc hai c\u1ee7a m\u1ed9t s\u1ed1 \u00e2m (tr\u1eeb tr\u01b0\u1eddng h\u1ee3p 0). V\u00ec v\u1eady, ch\u00fang ta c\u1ea7n \u0111\u1eb7t bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n (g\u1ecdi l\u00e0 radicand) l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0.[3] L\u01b0u \u00fd r\u1eb1ng quy t\u1eafc n\u00e0y kh\u00f4ng ch\u1ec9 \u00e1p d\u1ee5ng cho c\u0103n b\u1eadc hai m\u00e0 c\u00f2n cho t\u1ea5t c\u1ea3 c\u00e1c c\u0103n b\u1eadc ch\u1eb5n. Tuy nhi\u00ean, quy t\u1eafc n\u00e0y kh\u00f4ng \u00e1p d\u1ee5ng cho c\u0103n b\u1eadc l\u1ebb v\u00ec ho\u00e0n to\u00e0n h\u1ee3p l\u1ec7 khi c\u00f3 s\u1ed1 \u00e2m d\u01b0\u1edbi d\u1ea5u c\u0103n b\u1eadc l\u1ebb. Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x - 7 \u2265 0<\/span><\/p>\n<h3><b>3. Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm x<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 c\u00f4 l\u1eadp x \u1edf v\u1ebf tr\u00e1i c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea1n ch\u1ec9 c\u1ea7n c\u1ed9ng 7 v\u00e0o c\u1ea3 hai v\u1ebf. Sau \u0111\u00f3, b\u1ea1n s\u1ebd thu \u0111\u01b0\u1ee3c nh\u01b0 sau:[4]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x \u2265 7<\/span><\/p>\n<p><span style=\"font-weight: 400;\">M\u1eb9o chuy\u00ean gia<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Gi\u00e1o vi\u00ean To\u00e1n JOSEPH MEYER<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 gi\u1ea3i m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm x, b\u1ea1n c\u1ea7n thao t\u00e1c v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 c\u00f4 l\u1eadp x. S\u1eed d\u1ee5ng c\u00e1c k\u1ef9 thu\u1eadt nh\u01b0 t\u00ednh ch\u1ea5t ph\u00e2n ph\u1ed1i, r\u00fat g\u1ecdn c\u00e1c h\u1ea1ng t\u1eed c\u00f9ng lo\u1ea1i, ph\u00e2n t\u00edch th\u00e0nh th\u1eeba s\u1ed1, c\u1ed9ng ho\u1eb7c tr\u1eeb c\u00f9ng m\u1ed9t s\u1ed1, nh\u00e2n ho\u1eb7c chia cho c\u00f9ng m\u1ed9t s\u1ed1 kh\u00e1c 0 \u0111\u1ec3 c\u00f4 l\u1eadp \"x\" v\u00e0 t\u00ecm ra \u0111\u00e1p \u00e1n.<\/span><\/p>\n<h3><b>4. Bi\u1ec3u di\u1ec5n ch\u00ednh x\u00e1c t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 c\u00e1ch vi\u1ebft t\u1eadp x\u00e1c \u0111\u1ecbnh:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">D = [7,\u221e)<\/span><\/p>\n<h3><b>5. T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m c\u00f3 ch\u1ee9a c\u0103n b\u1eadc hai khi c\u00f3 nhi\u1ec1u nghi\u1ec7m<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3 s\u1eed b\u1ea1n \u0111ang gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n v\u1edbi h\u00e0m s\u1ed1 sau: Y = 1\/\u221a(x\u00b2 - 4). Khi b\u1ea1n ph\u00e2n t\u00edch m\u1eabu s\u1ed1 v\u00e0 \u0111\u1eb7t n\u00f3 b\u1eb1ng 0, b\u1ea1n s\u1ebd thu \u0111\u01b0\u1ee3c x \u2260 (2, -2). \u0110\u00e2y l\u00e0 c\u00e1ch x\u1eed l\u00fd ti\u1ebfp theo:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e2y gi\u1edd, h\u00e3y ki\u1ec3m tra v\u00f9ng d\u01b0\u1edbi -2 (v\u00ed d\u1ee5 nh\u01b0 thay x b\u1eb1ng -3), \u0111\u1ec3 xem c\u00e1c s\u1ed1 nh\u1ecf h\u01a1n -2 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o m\u1eabu s\u1ed1 \u0111\u1ec3 cho k\u1ebft qu\u1ea3 l\u1edbn h\u01a1n 0 hay kh\u00f4ng. Ch\u00fang c\u00f3 th\u1ec3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(-3)\u00b2 - 4 = 5<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e2y gi\u1edd, h\u00e3y ki\u1ec3m tra v\u00f9ng gi\u1eefa -2 v\u00e0 2. Ch\u1eb3ng h\u1ea1n, ch\u1ecdn x = 0.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">0\u00b2 - 4 = -4, do \u0111\u00f3 c\u00e1c s\u1ed1 gi\u1eefa -2 v\u00e0 2 kh\u00f4ng th\u1ecfa m\u00e3n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e2y gi\u1edd, th\u1eed m\u1ed9t s\u1ed1 l\u1edbn h\u01a1n 2, ch\u1eb3ng h\u1ea1n nh\u01b0 3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">3\u00b2 - 4 = 5, do \u0111\u00f3 c\u00e1c s\u1ed1 l\u1edbn h\u01a1n 2 th\u1ecfa m\u00e3n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sau khi ho\u00e0n th\u00e0nh, h\u00e3y vi\u1ebft t\u1eadp x\u00e1c \u0111\u1ecbnh. \u0110\u00e2y l\u00e0 c\u00e1ch vi\u1ebft t\u1eadp x\u00e1c \u0111\u1ecbnh:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">D = (-\u221e, -2) U (2, \u221e)<\/span><\/p>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 4: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1eed d\u1ee5ng logarit t\u1ef1 nhi\u00ean (ln)<\/b><\/h2>\n<h3><b>1. Vi\u1ebft b\u00e0i to\u00e1n<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Gi\u1ea3 s\u1eed b\u1ea1n \u0111ang gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">f(x) = ln(x - 8)<\/span><\/p>\n<div id=\"attachment_24282\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img aria-describedby=\"caption-attachment-24282\" loading=\"lazy\" class=\"size-full wp-image-24282\" src=\"https:\/\/www.hostify.vn\/blog\/wp-content\/uploads\/2024\/06\/domain-of-a-function-3.png\" alt=\"T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1eed d\u1ee5ng logarit t\u1ef1 nhi\u00ean (ln)\" width=\"800\" height=\"600\" \/><p id=\"caption-attachment-24282\" class=\"wp-caption-text\">T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1eed d\u1ee5ng logarit t\u1ef1 nhi\u00ean (ln)<\/p><\/div>\n<h3><b>2. \u0110\u1eb7t bi\u1ec3u th\u1ee9c trong ngo\u1eb7c l\u1edbn h\u01a1n 0<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Logarit t\u1ef1 nhi\u00ean (ln) ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 d\u01b0\u01a1ng,[5] v\u00ec v\u1eady, c\u1ea7n \u0111\u1eb7t bi\u1ec3u th\u1ee9c trong ngo\u1eb7c l\u1edbn h\u01a1n 0 \u0111\u1ec3 \u0111\u00e1p \u1ee9ng \u0111i\u1ec1u ki\u1ec7n n\u00e0y. Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x - 8 &gt; 0<\/span><\/p>\n<h3><b>3. Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 c\u00f4 l\u1eadp x, b\u1ea1n ch\u1ec9 c\u1ea7n c\u1ed9ng 8 v\u00e0o c\u1ea3 hai v\u1ebf.[6] Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x - 8 + 8 &gt; 0 + 8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">x &gt; 8<\/span><\/p>\n<h3><b>4. Bi\u1ec3u di\u1ec5n t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 l\u1edbn h\u01a1n 8 cho \u0111\u1ebfn d\u01b0\u01a1ng v\u00f4 c\u1ef1c.[7] Th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">D = (8,\u221e)<\/span><\/p>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 5: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1eed d\u1ee5ng \u0111\u1ed3 th\u1ecb<\/b><\/h2>\n<h3><b>1. Quan s\u00e1t \u0111\u1ed3 th\u1ecb<\/b><\/h3>\n<h3><b>2. Ki\u1ec3m tra c\u00e1c gi\u00e1 tr\u1ecb x xu\u1ea5t hi\u1ec7n tr\u00ean \u0111\u1ed3 th\u1ecb<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110i\u1ec1u n\u00e0y c\u00f3 v\u1ebb kh\u00f3 kh\u0103n nh\u01b0ng \u0111\u00e2y l\u00e0 m\u1ed9t v\u00e0i m\u1eb9o:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng th\u1eb3ng: N\u1ebfu b\u1ea1n th\u1ea5y m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng th\u1eb3ng \u0111\u1ee9ng tr\u00ean \u0111\u1ed3 th\u1ecb k\u00e9o d\u00e0i v\u00f4 c\u1ef1c theo c\u1ea3 hai h\u01b0\u1edbng, th\u00ec v\u1ec1 c\u01a1 b\u1ea3n m\u1ecdi gi\u00e1 tr\u1ecb x \u0111\u1ec1u \u0111\u01b0\u1ee3c bao ph\u1ee7. Do \u0111\u00f3, t\u1eadp x\u00e1c \u0111\u1ecbnh b\u1eb1ng t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Parabol th\u00f4ng th\u01b0\u1eddng: N\u1ebfu b\u1ea1n th\u1ea5y m\u1ed9t parabol h\u01b0\u1edbng l\u00ean tr\u00ean ho\u1eb7c h\u01b0\u1edbng xu\u1ed1ng d\u01b0\u1edbi, th\u00ec \u0111\u00fang, t\u1eadp x\u00e1c \u0111\u1ecbnh s\u1ebd l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c, v\u00ec cu\u1ed1i c\u00f9ng t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 tr\u00ean tr\u1ee5c ho\u00e0nh \u0111\u1ec1u \u0111\u01b0\u1ee3c bao ph\u1ee7.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Parabol n\u1eb1m ngang: B\u00e2y gi\u1edd, n\u1ebfu b\u1ea1n c\u00f3 m\u1ed9t parabol c\u00f3 \u0111\u1ec9nh (4,0) m\u1edf r\u1ed9ng v\u00f4 c\u1ef1c sang ph\u1ea3i, th\u00ec t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a b\u1ea1n l\u00e0 D = [4,\u221e).<\/span><\/li>\n<\/ul>\n<h3><b>3. Bi\u1ec3u di\u1ec5n t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Ch\u1ec9 c\u1ea7n bi\u1ec3u di\u1ec5n t\u1eadp x\u00e1c \u0111\u1ecbnh d\u1ef1a tr\u00ean lo\u1ea1i \u0111\u1ed3 th\u1ecb b\u1ea1n \u0111ang l\u00e0m vi\u1ec7c. N\u1ebfu b\u1ea1n kh\u00f4ng ch\u1eafc ch\u1eafn v\u00e0 bi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng, h\u00e3y thay c\u00e1c gi\u00e1 tr\u1ecb x tr\u1edf l\u1ea1i v\u00e0o h\u00e0m \u0111\u1ec3 ki\u1ec3m tra.<\/span><\/p>\n<h2><b>Ph\u01b0\u01a1ng ph\u00e1p 6: T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1eed d\u1ee5ng quan h\u1ec7<\/b><\/h2>\n<h3><b>1. Li\u1ec7t k\u00ea c\u00e1c quan h\u1ec7<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Quan h\u1ec7 l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c c\u1eb7p s\u1ed1 \u0111\u01b0\u1ee3c s\u1eafp th\u1ee9 t\u1ef1. Gi\u1ea3 s\u1eed b\u1ea1n \u0111ang l\u00e0m vi\u1ec7c v\u1edbi c\u00e1c c\u1eb7p t\u1ecda \u0111\u1ed9 sau: {(1, 3), (2, 4), (5, 7)}<\/span><\/p>\n<h3><b>2. Li\u1ec7t k\u00ea c\u00e1c gi\u00e1 tr\u1ecb x<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00e1c gi\u00e1 tr\u1ecb x n\u00e0y l\u00e0: 1, 2, 5.[10]<\/span><\/p>\n<h3><b>3. Bi\u1ec3u di\u1ec5n t\u1eadp x\u00e1c \u0111\u1ecbnh<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">T\u1eadp x\u00e1c \u0111\u1ecbnh D = {1, 2, 5}<\/span><\/p>\n<h3><b>4. Ki\u1ec3m tra t\u00ednh ch\u1ea5t l\u00e0 h\u00e0m<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 m\u1ed9t quan h\u1ec7 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m, th\u00ec v\u1edbi m\u1ed7i gi\u00e1 tr\u1ecb x \u0111\u1ea7u v\u00e0o, b\u1ea1n ch\u1ec9 nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t gi\u00e1 tr\u1ecb y t\u01b0\u01a1ng \u1ee9ng. V\u00ec v\u1eady, n\u1ebfu b\u1ea1n \u0111\u1eb7t x b\u1eb1ng 3, b\u1ea1n lu\u00f4n ph\u1ea3i nh\u1eadn \u0111\u01b0\u1ee3c y b\u1eb1ng 6, v.v. Quan h\u1ec7 {(1,4), (3,5), (1,5)} kh\u00f4ng ph\u1ea3i l\u00e0 h\u00e0m v\u00ec gi\u00e1 tr\u1ecb x b\u1eb1ng 1 c\u00f3 hai gi\u00e1 tr\u1ecb y t\u01b0\u01a1ng \u1ee9ng kh\u00e1c nhau l\u00e0 4 v\u00e0 5.<\/span><\/p>\n<h2><b>K\u1ebft lu\u1eadn<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a m\u1ed9t h\u00e0m l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u v\u00e0o h\u1ee3p l\u1ec7 c\u1ee7a h\u00e0m. N\u00f3i c\u00e1ch kh\u00e1c, n\u00f3 l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb x m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 thay v\u00e0o h\u00e0m m\u00e0 kh\u00f4ng g\u1eb7p l\u1ed7i. L\u01b0u \u00fd r\u1eb1ng t\u1eadp x\u00e1c \u0111\u1ecbnh c\u00f3 th\u1ec3 kh\u00e1c v\u1edbi t\u1eadp gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m. T\u1eadp gi\u00e1 tr\u1ecb l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb \u0111\u1ea7u ra c\u00f3 th\u1ec3 c\u1ee7a h\u00e0m.<\/span><\/p>\n<div class=\"tg_wrap_cbsv tg_wrap_cbsv_blue\" style=\"margin: 20px 0px; border-radius: 4px; border: 2px solid #0066b2;\"><cite style=\"margin: 0px; background-color: #0066b2; color: #fff; border-top-left-radius: 2px; border-top-right-radius: 2px; font-size: 19px; padding: 12px 20px; font-weight: bold; display: block; font-style: normal;\">B\u1ea1n \u0111ang mu\u1ed1n x\u00e2y d\u1ef1ng m\u1ed9t trang web c\u1ee7a ri\u00eang m\u00ecnh<\/cite><\/p>\n<div class=\"textwidget\" style=\"padding: 20px; background: #70c2e280;\">\u0110\u0103ng k\u00fd ngay t\u00ean mi\u1ec1n th\u01b0\u01a1ng hi\u1ec7u t\u1ea1i Tenten.vn ch\u1ec9 v\u1edbi 2 c\u00fa click chu\u1ed9t: <strong>Ki\u1ec3m tra s\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a t\u00ean mi\u1ec1n: Nh\u1eadp t\u00ean mi\u1ec1n v\u00e0 nh\u1ea5n \"ki\u1ec3m tra\".<\/strong> <span style=\"color: #ffff00;\"><a class=\"btn_combi_sv\" style=\"font-weight: bold; color: #ffff00; padding: 8px 26px 8px 26px; font-size: 20px; line-height: 30px; border-radius: 56px; text-shadow: none; background: #0066b2; display: table; margin: 0px auto;\" href=\"https:\/\/tenten.vn\/vi\/bang-gia-ten-mien?code=knjcpEfWoTSzUNMw&amp;idCampaign=3080\">B\u1ea2NG GI\u00c1 T\u00caN MI\u1ec0N M\u1edaI NH\u1ea4T<\/a><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/bit.ly\/3QYbaqa\">V\u00e0o nh\u00f3m Zalo nh\u1eadn \u01b0u \u0111\u00e3i t\u00ean mi\u1ec1n t\u1ea1i \u0111\u00e2y<\/a><\/li>\n<li>Hotline: (024) 71 089 999<\/li>\n<li>Email: info@tenten.vn<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h4><strong>B\u00e0i li\u00ean quan<\/strong><\/h4>\n<ul>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/domain\/\">Domain l\u00e0 g\u00ec? H\u01b0\u1edbng d\u1eabn \u0111\u0103ng k\u00fd t\u00ean mi\u1ec1n t\u1eeb A-Z<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-la-gi\/\">T\u00ean mi\u1ec1n l\u00e0 g\u00ec? Nh\u1eefng l\u01b0u \u00fd khi s\u1eed d\u1ee5ng d\u1ecbch v\u1ee5 t\u00ean mi\u1ec1n<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-vn\/\">T\u00ean mi\u1ec1n vn: L\u1ee3i \u00edch &amp; \u01afu \u0111i\u1ec3m c\u1ee7a t\u00ean mi\u1ec1n Vi\u1ec7t Nam<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-vn-2\/\">T\u00ean mi\u1ec1n .vn l\u00e0 g\u00ec? N\u00ean mua t\u00ean mi\u1ec1n .vn \u1edf \u0111\u00e2u r\u1ebb nh\u1ea5t?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-com-vn\/\">T\u00ean mi\u1ec1n .com.vn l\u00e0 g\u00ec? N\u00ean ch\u1ecdn t\u00ean mi\u1ec1n .com.vn hay .vn?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-edu-vn\/\">T\u00ean mi\u1ec1n Edu.vn l\u00e0 c\u00e1nh c\u1ed5ng truy\u1ec1n t\u1ea3i tri th\u1ee9c tr\u1ef1c tuy\u1ebfn<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-biz-vn-2\/\">\u00dd ngh\u0129a t\u00ean mi\u1ec1n biz vn v\u00e0 l\u1ee3i th\u1ebf khi d\u00f9ng .biz.vn cho doanh nghi\u1ec7p<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-name-vn\/\">T\u1eeb A-Z v\u1ec1 t\u00ean mi\u1ec1n name.vn, \u0111\u0103ng k\u00fd name.vn \u1edf \u0111\u00e2u r\u1ebb v\u00e0 uy t\u00edn?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-ai-vn\/\">T\u00ean mi\u1ec1n ai.vn l\u00e0 g\u00ec? Mang l\u1ea1i l\u1ee3i \u00edch g\u00ec khi s\u1eed d\u1ee5ng?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-id-vn\/\">T\u00ean mi\u1ec1n id.vn l\u00e0 g\u00ec? L\u1ee3i \u00edch khi s\u1eed d\u1ee5ng t\u00ean mi\u1ec1n id.vn<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-io-vn\/\">T\u00ean mi\u1ec1n io.vn l\u00e0 g\u00ec? Mang l\u1ea1i l\u1ee3i \u00edch g\u00ec khi s\u1eed d\u1ee5ng?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-net\/\">T\u00ean mi\u1ec1n .net l\u00e0 g\u00ec? L\u1ee3i \u00edch khi s\u1eed d\u1ee5ng t\u00ean mi\u1ec1n .net gi\u00e1 r\u1ebb<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-info\/\">T\u00ean mi\u1ec1n .info l\u00e0 g\u00ec? N\u00ean mua t\u00ean mi\u1ec1n .info \u1edf \u0111\u00e2u r\u1ebb nh\u1ea5t<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/chon-ten-mien\/\">M\u1ed9t s\u1ed1 c\u00f4ng c\u1ee5 ch\u1ecdn t\u00ean mi\u1ec1n thu h\u00fat m\u1ecdi kh\u00e1ch h\u00e0ng<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/ten-mien-chuan-seo\/\">T\u00ean mi\u1ec1n chu\u1ea9n SEO c\u1ea7n \u0111\u00e1p \u1ee9ng ti\u00eau ch\u00ed n\u00e0o? H\u01b0\u1edbng d\u1eabn c\u00e1ch ch\u1ecdn t\u00ean mi\u1ec1n<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/nha-cung-cap-ten-mien\/\">Top c\u00e1c nh\u00e0 cung c\u1ea5p t\u00ean mi\u1ec1n uy t\u00edn. N\u00ean ch\u1ecdn \u0111\u01a1n v\u1ecb n\u00e0o?<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/dau-tu-ten-mien\/\">B\u00ed quy\u1ebft \u0111\u1ea7u t\u01b0 t\u00ean mi\u1ec1n t\u1ea1o n\u00ean gi\u00e1 tr\u1ecb cao<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/cach-dang-ky-ten-mien-mien-phi\/\">C\u00e1ch \u0111\u0103ng k\u00fd t\u00ean mi\u1ec1n mi\u1ec5n ph\u00ed: \u0110\u01a1n gi\u1ea3n, ai c\u0169ng l\u00e0m \u0111\u01b0\u1ee3c<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/mua-ban-ten-mien\/\">H\u01b0\u1edbng d\u1eabn mua b\u00e1n t\u00ean mi\u1ec1n chi ti\u1ebft cho ng\u01b0\u1eddi m\u1edbi<\/a><\/li>\n<li><a href=\"https:\/\/cloud.z.com\/vn\/news\/bao-mat-ten-mien-la-gi\/\">B\u1ea3o m\u1eadt t\u00ean mi\u1ec1n l\u00e0 g\u00ec? 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N\u00f3i c\u00e1ch kh\u00e1c, n\u00f3 l\u00e0 t\u1eadp h\u1ee3p c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a x m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 thay v\u00e0o b\u1ea5t k\u1ef3 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o...<\/p>\n","protected":false},"author":28,"featured_media":10909,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[177,83],"tags":[],"jetpack_featured_media_url":"https:\/\/cloud.z.com\/vn\/wp-content\/uploads\/2024\/06\/domain-of-a-function.png","_links":{"self":[{"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/posts\/10869"}],"collection":[{"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/users\/28"}],"replies":[{"embeddable":true,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/comments?post=10869"}],"version-history":[{"count":3,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/posts\/10869\/revisions"}],"predecessor-version":[{"id":10910,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/posts\/10869\/revisions\/10910"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/media\/10909"}],"wp:attachment":[{"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/media?parent=10869"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/categories?post=10869"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cloud.z.com\/vn\/en\/wp-json\/wp\/v2\/tags?post=10869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}