{"id":29063,"date":"2021-06-26T13:00:55","date_gmt":"2021-06-26T13:00:55","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29063"},"modified":"2024-09-22T07:03:14","modified_gmt":"2024-09-22T07:03:14","slug":"%e4%bb%a3%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%ae%9a%e4%b9%89%e5%9f%9f%e3%80%81%e5%80%bc%e5%9f%9f%e5%92%8c%e5%9b%be%e5%83%8f","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e4%bb%a3%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%ae%9a%e4%b9%89%e5%9f%9f%e3%80%81%e5%80%bc%e5%9f%9f%e5%92%8c%e5%9b%be%e5%83%8f\/","title":{"rendered":"\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf"},"content":{"rendered":"<p><center><\/p>\n<h1>\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n\u672c\u8bfe\u4ecb\u7ecd\u4e86\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6982\u5ff5\uff0c\u5e76\u5c06\u8fd9\u4e9b\u6982\u5ff5\u5e94\u7528\u4e8e\u4ee3\u6570\u51fd\u6570\u7684\u5b9e\u9645\u4f8b\u5b50\u4e2d\u3002\u6211\u4eec\u5c06\u5ba1\u67e5\u7528\u4e8e\u786e\u5b9a\u8fd9\u4e9b\u5143\u7d20\u7684\u56fe\u5f62\u548c\u5206\u6790\u6280\u672f\u3002<br \/>\n<\/em><br \/>\n<strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f <\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u6b63\u786e\u5b9a\u4e49<\/strong>\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u56fe\u5f62\u65b9\u6cd5\u6765\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u548c\u503c\u57df\u3002<\/li>\n<li><strong>\u6784\u5efa<\/strong>\u7b26\u53f7\u8868\u6765\u5206\u6790\u51fd\u6570\u7684\u884c\u4e3a\u3002<\/li>\n<\/ol>\n<p><\/center><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/zhb8GKlcdA8\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<h2>\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u5b9a\u4e49<\/h2>\n<p style=\"text-align: justify;\">\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u5bf9\u7ebf\u6027\u51fd\u6570\u3001\u4e8c\u6b21\u51fd\u6570\u53ca\u5176\u7c7b\u4f3c\u51fd\u6570\u8fdb\u884c\u4e86\u76f8\u5f53\u8be6\u7ec6\u7684\u7814\u7a76\u3002\u6211\u4eec\u8fd8\u7814\u7a76\u4e86\u76f4\u7ebf\u3001\u629b\u7269\u7ebf\u3001\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u7b49\u66f2\u7ebf\uff0c\u4ee5\u53ca\u591a\u9879\u5f0f\u548c\u4e00\u822c\u4ee3\u6570\u51fd\u6570\u7684\u64cd\u4f5c\u3002\u5b8c\u6210\u8fd9\u4e9b\u5185\u5bb9\u540e\uff0c\u73b0\u5728\u66f4\u5bb9\u6613\u6df1\u5165\u7406\u89e3\u5173\u4e8e\u51fd\u6570\u7684\u4e00\u4e9b\u66f4\u57fa\u7840\u7684\u65b9\u9762\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u8fd9\u6b21\u5c06\u8981\u5ba1\u67e5\u7684\u5185\u5bb9\uff0c\u9996\u5148\u5f15\u5165<strong>\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf<\/strong>\u7684\u6982\u5ff5\u3002<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=306s\" target=\"_blank\" rel=\"noopener\"><strong>\u8bbe <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u4e3a\u4e00\u4e2a\u5b9a\u4e49\u5728\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u4e4b\u95f4\u7684\u51fd\u6570<\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{matrix}f &amp; : &amp; A &amp; \\longrightarrow &amp; B \\\\ &amp; &amp; x &amp; \\longmapsto &amp; y=f(x)\n\n\\end{matrix}<\/span>\n<p style=\"text-align: justify;\">\u96c6\u5408 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u5206\u522b\u79f0\u4e3a\u201c\u8f93\u5165\u96c6\u201d\u548c\u201c\u8f93\u51fa\u96c6\u201d\u3002\u57fa\u4e8e\u8fd9\u4e9b\u96c6\u5408\uff0c\u5b9a\u4e49\u4e86\u4ee5\u4e0b\u96c6\u5408\uff1a<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(f) = \\{x\\in A\\;|\\; (\\exists y \\in B)(y=f(x))\\}<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(f) = \\{y\\in B\\;|\\; (\\exists ! x \\in Dom(f))(y=f(x))\\}<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Graf(f) = \\{(x,y)\\in A\\times B\\;|\\; x\\in Dom(f) \\wedge y=f(x) \\}<\/span>\n<h2>\u793a\u4f8b\u5206\u6790<\/h2>\n<p style=\"text-align: justify;\">\u867d\u7136\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6982\u5ff5\u672c\u8d28\u4e0a\u662f\u7406\u8bba\u95ee\u9898\uff0c\u4f46\u5b83\u4eec\u7684\u7406\u89e3\u66f4\u591a\u4f9d\u8d56\u4e8e\u5b9e\u9645\u4f8b\u5b50\u7684\u5e94\u7528\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u5206\u6790\u4ee5\u4e0b\u4e09\u4e2a\u6848\u4f8b\u6765\u5c55\u793a\u8fd9\u4e9b\u6982\u5ff5\u7684\u5e94\u7528\uff1a<\/p>\n<h3>\u8ba1\u7b97\uff1a <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\sqrt{1-x^2}<\/span> \u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=560s\" target=\"_blank\" rel=\"noopener\"><strong>\u8ba9\u6211\u4eec\u5f00\u59cb\u5206\u6790<\/strong><\/a> \u5199\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span> \u3002\u5982\u679c\u6211\u4eec\u8fd9\u6837\u505a\uff0c\u5c31\u4f1a\u5f97\u5230\u4ee5\u4e0b\u65b9\u7a0b<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y = \\sqrt{1-x^2}<\/span>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u5c06\u6b64\u8868\u8fbe\u5f0f\u5e73\u65b9\uff0c\u6211\u4eec\u5f88\u5feb\u5c31\u4f1a\u5f97\u51fa\u4e00\u4e2a\u6211\u4eec\u5df2\u7ecf\u719f\u6089\u7684\u65b9\u7a0b<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n&amp; y^2 = 1-x^2 \\\\\n\n\\equiv &amp; x^2 + y^2 = 1 \\end{array}<\/span>\n<p style=\"text-align: justify;\">\u8fd9\u662f\u5355\u4f4d\u5706\u7684\u65b9\u7a0b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-DQGthMyBY6g\/YNVVrnVQEfI\/AAAAAAAAFOQ\/6_lf8fRQdDIT9NMqstyLOJ2F7nQM9pc8ACLcBGAsYHQ\/s0\/circulounitario.PNG\" alt=\"\u5355\u4f4d\u5706\u53ca\u5176\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\" class=\"aligncenter lazyload\" width=\"245\" height=\"249\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-DQGthMyBY6g\/YNVVrnVQEfI\/AAAAAAAAFOQ\/6_lf8fRQdDIT9NMqstyLOJ2F7nQM9pc8ACLcBGAsYHQ\/s0\/circulounitario.PNG\" alt=\"\u5355\u4f4d\u5706\u53ca\u5176\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\" class=\"aligncenter lazyload\" width=\"245\" height=\"249\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u7136\u800c\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u5fc5\u987b\u5c0f\u5fc3\uff0c\u56e0\u4e3a\u5e73\u65b9\u64cd\u4f5c\u201c\u589e\u52a0\u4e86\u4e00\u4e9b\u4fe1\u606f\u201d\u3002\u4ece\u4ee3\u6570\u4e0a\u8bb2\uff0c\u6709\u4e24\u4e2a\u503c\u6ee1\u8db3\u201c\u662f\u5e73\u65b9\u6839\u201d\u7684\u6761\u4ef6\uff0c\u4f46\u5728\u5206\u6790\u5f00\u59cb\u65f6\uff0c\u5e73\u65b9\u6839\u88ab\u6307\u5b9a\u4e3a\u4e00\u4e2a\u51fd\u6570\uff0c\u51fd\u6570\u53ea\u80fd\u6709\u4e00\u4e2a\u7ed3\u679c\u3002\u6211\u4eec\u8ba8\u8bba\u7684\u662f\u4e3b\u6839\u3002\u56e0\u6b64\uff0c\u6700\u521d\u7684\u8868\u8ff0\u4ec5\u6307\u5355\u4f4d\u5706\u7684\u4e0a\u534a\u90e8\u5206\uff0c\u800c\u4e0d\u662f\u5b8c\u6574\u7684\u56fe\u5f62\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-AxSf-9lgnuE\/YNVbSJpd-rI\/AAAAAAAAFOg\/0APXEMWIFpAm8DX9651iD6wcq5bTJwFoQCLcBGAsYHQ\/s0\/circulounitario%2B2.PNG\" alt=\"\u5355\u4f4d\u5706\u53ca\u5176\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\" class=\" aligncenter lazyload\" width=\"401\" height=\"361\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-AxSf-9lgnuE\/YNVbSJpd-rI\/AAAAAAAAFOg\/0APXEMWIFpAm8DX9651iD6wcq5bTJwFoQCLcBGAsYHQ\/s0\/circulounitario%2B2.PNG\" alt=\"\u5355\u4f4d\u5706\u53ca\u5176\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\" class=\" aligncenter lazyload\" width=\"401\" height=\"361\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u6839\u636e\u8fd9\u4e2a\u56fe\u50cf\uff0c\u5f88\u660e\u663e<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(f) = \\{x\\in\\mathbb{R}\\;|\\; |x|\\leq 1\\} = [-1,1]<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(f) = \\{y\\in\\mathbb{R}\\;|\\; 0\\leq y\\leq 1\\} = [0,1]<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Graf(f) = \\{(x,y)\\in \\mathbb{R}\\times \\mathbb{R}\\;|\\; x\\in [-1,1] \\wedge y=\\sqrt{1-x^2}\\}<\/span>\n<p style=\"text-align: justify;\">\u867d\u7136\u6211\u4ece\u56fe\u5f62\u7684\u89d2\u5ea6\u8fdb\u884c\u4e86\u5206\u6790\uff0c\u4f46\u4e5f\u53ef\u4ee5\u901a\u8fc7\u590d\u4e60\u76f8\u5173\u64cd\u4f5c\uff0c\u4ece\u66f4\u5206\u6790\u7684\u89d2\u5ea6\u8fdb\u884c\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\color{red}{\\sqrt{{1-x^2}}}<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">1-x^2<\/span> \u5bf9\u6240\u6709\u5b9e\u6570\u90fd\u5b9a\u4e49\u826f\u597d\u3002<\/p>\n<p style=\"text-align: justify;\">\u7136\u800c\uff0c\u5e73\u65b9\u6839\u4ec5\u63a5\u53d7\u5927\u4e8e\u6216\u7b49\u4e8e\u96f6\u7684\u503c\u3002<\/p>\n<p style=\"text-align: justify;\">\u7531\u6b64\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rlrl}\n\nx\\in Dom(f) &amp; \\leftrightarrow &amp; 0 &amp;\\leq 1-x^2 \\\\\n\n{} &amp; \\leftrightarrow &amp; x^2 &amp;\\leq 1 \\\\\n\n&amp; \\leftrightarrow &amp; |x| &amp;\\leq 1 \\\\\n\n&amp; \\leftrightarrow &amp; -1 &amp;\\leq x \\leq 1 \\\\\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\u56e0\u6b64:\\; Dom(f) = \\{x\\in \\mathbb{R}\\;|x| \\leq 1\\} = [-1,1]\n<\/span>\n<p style=\"text-align: justify;\">\u786e\u5b9a\u503c\u57df\u7684\u5206\u6790\u65b9\u6cd5\u901a\u5e38\u590d\u6742\u5f97\u591a\uff1b\u6700\u7b80\u5355\u7684\u60c5\u51b5\u901a\u8fc7\u627e\u5230\u53cd\u51fd\u6570\u6765\u89e3\u51b3\uff0c\u4f46\u5728\u8be6\u7ec6\u5ba1\u67e5\u8be5\u4e3b\u9898\u4e4b\u524d\uff0c\u5efa\u8bae\u9996\u5148\u7814\u7a76\u51fd\u6570\u7684\u590d\u5408\u4ee5\u53ca\u5176\u4ed6\u66f4\u7b80\u5355\u7684\u60c5\u51b5\uff0c\u4ee5\u5efa\u7acb\u575a\u5b9e\u7684\u57fa\u7840\u3002\u540c\u65f6\uff0c\u6211\u4eec\u5373\u5c06\u5ba1\u67e5\u7684\u56fe\u5f62\u65b9\u6cd5\u5c06\u6db5\u76d6\u786e\u5b9a\u503c\u57df\u7684\u5927\u90e8\u5206\u96be\u70b9\u3002<\/p>\n<h3>\u5206\u6790\uff1a <span class=\"katex-eq\" data-katex-display=\"false\">g(x) =\\displaystyle \\frac{x^2 - 1}{x^2 + 1}<\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u79cd\u5feb\u901f\u627e\u5230<\/strong><\/a>\u51fd\u6570\u5b9a\u4e49\u57df\u7684\u65b9\u6cd5\u662f\u8be2\u95ee\u54ea\u4e9b <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u503c\u4f1a\u201c\u7834\u574f\u51fd\u6570\u201d\u3002\u663e\u7136\uff0c\u53ea\u6709\u5f53\u5206\u6bcd\u4e3a\u96f6\u65f6\uff0c\u51fd\u6570\u624d\u4f1a\u5931\u6548\u3002\u5373\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n&amp; x^2 + 1 = 0 \\\\\n\n\\equiv &amp; x^2 = -1 \\\\\n\n\\end{array}<\/span>\n<p style=\"text-align: justify;\">\u7531\u4e8e\u6ca1\u6709\u5b9e\u6570\u53ef\u4ee5\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\uff0c\u5f88\u663e\u7136<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\color{blue}{Dom(g) = \\mathbb{R}}<\/span>\n<p style=\"text-align: justify;\">\u786e\u5b9a\u56fe\u50cf\u901a\u5e38\u662f\u786e\u5b9a\u51fd\u6570\u503c\u57df\u7684\u6700\u5feb\u65b9\u6cd5\uff1b\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c<a href=\"https:\/\/toposuranos.com\/algebra-de-polinomios-de-numeros-reais\/\" rel=\"noopener\" target=\"_blank\">\u591a\u9879\u5f0f\u9664\u6cd5<\/a>\u5c06\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u5de5\u5177\u3002<\/p>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fdb\u884c\u591a\u9879\u5f0f\u9664\u6cd5\uff0c\u6211\u4eec\u5f97\u51fa\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y= \\displaystyle\\frac{x^2-1}{x^2+1} =<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">-\\displaystyle\\frac{2}{x^2 + 1}<\/span>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u5c06\u539f\u59cb\u51fd\u6570\u5206\u89e3\u4e3a\u4e24\u90e8\u5206\u66f4\u7b80\u5355\u7684\u90e8\u5206\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u6574\u6570\u90e8\u5206\u201d\u548c\u201c\u5206\u6570\u90e8\u5206\u201d\u3002\u5206\u522b\u7ed8\u5236\u8fd9\u4e9b\u90e8\u5206\u7684\u56fe\u50cf\u6bd4\u4e00\u6b21\u6027\u7ed8\u5236\u539f\u59cb\u51fd\u6570\u7684\u56fe\u50cf\u8981\u5bb9\u6613\u5f97\u591a\u3002<\/p>\n<h3>\u5206\u6790\uff1a <span class=\"katex-eq\" data-katex-display=\"false\">h(x) =\\displaystyle \\frac{x - 1}{\\sqrt{x+1}}<\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=1580s\" target=\"_blank\" rel=\"noopener\"><strong>\u4ee3\u6570\u5206\u6790 <\/strong><\/a>\u5c06\u6709\u52a9\u4e8e\u5feb\u901f\u786e\u5b9a\u8be5\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002\u53ea\u9700\u6ce8\u610f\u5b83\u5c06\u5728\u4ee5\u4e0b\u60c5\u51b5\u4e0b\u5b9a\u4e49\u826f\u597d\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rrl}\n\n&amp; 0 &amp; \\lt x + 1 \\\\\n\n\\equiv &amp; -1 &amp; \\lt x \\\\\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u5f88\u660e\u663e <span class=\"katex-eq\" data-katex-display=\"false\">Dom(h)=]-1,+\\infty[.<\/span>\n<p style=\"text-align: justify;\">\u4e3a\u4e86\u627e\u5230\u503c\u57df\uff0c\u6700\u597d\u7ed8\u5236\u56fe\u50cf\uff0c\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u5c06\u4f7f\u7528<strong>\u7b26\u53f7\u8868<\/strong>\u3002\u51fd\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span> \u7531\u4e24\u90e8\u5206\u7ec4\u6210<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=\\displaystyle\\frac{\\color{green}{x-1}}{\\color{red}{\\sqrt{x+1}}}<\/span>\n<p style=\"text-align: justify;\">\u4e0a\u9762\u7684\u90e8\u5206\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">x=1<\/span> \u65f6\u4e3a\u96f6\uff1b\u4e0b\u9762\u7684\u90e8\u5206\u4e0d\u4ec5\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">x=-1<\/span> \u65f6\u4e3a\u96f6\uff0c\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">x\\lt-1<\/span> \u65f6\u4e5f\u672a\u5b9a\u4e49\u3002\u6839\u636e\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6784\u5efa\u4e86\u4ee5\u4e0b\u7b26\u53f7\u8868\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\infty<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">+1<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">+\\infty<\/span><\/th>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x-1<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\infty <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} +\\infty <\/span><\/td>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x+1}<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u4e0d\u5b58\u5728  <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u4e0d\u5b58\u5728 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} + <\/span><\/td>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{x-1}{\\sqrt{x+1}}<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u4e0d\u5b58\u5728 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{}\u4e0d\u5b58\u5728 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> -\\infty <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} +\\infty <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u6839\u636e\u8868\u4e2d\u7684\u4fe1\u606f\uff0c\u73b0\u5728\u7ed8\u5236\u51fd\u6570\u56fe\u50cf\u53d8\u5f97\u975e\u5e38\u7b80\u5355\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-mWc6Hza3Wl0\/YNWMYho7pPI\/AAAAAAAAFO4\/0D8zrIeKcc8HY7hlWuvJOWDnYE6Zw--cQCLcBGAsYHQ\/s0\/grafico%2B2.PNG\" alt=\"\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u7b26\u53f7\u8868\u7684\u56fe\u50cf\" class=\" aligncenter lazyload\" width=\"498\" height=\"310\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-mWc6Hza3Wl0\/YNWMYho7pPI\/AAAAAAAAFO4\/0D8zrIeKcc8HY7hlWuvJOWDnYE6Zw--cQCLcBGAsYHQ\/s0\/grafico%2B2.PNG\" alt=\"\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u7b26\u53f7\u8868\u7684\u56fe\u50cf\" class=\" aligncenter lazyload\" width=\"498\" height=\"310\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u8fd9\u4e9b\u4fe1\u606f\uff0c\u73b0\u5728\u786e\u5b9a\u5b9a\u4e49\u57df\u548c\u503c\u57df\u5c31\u53d8\u5f97\u5f88\u7b80\u5355\u4e86\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(h)=]-1,+\\infty[<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(h)=\\mathbb{R}<\/span>\n<h3>\u5efa\u8bae\u7ec3\u4e60<\/h3>\n<p style=\"text-align: justify;\">\u4f7f\u7528\u6211\u4eec\u521a\u521a\u5ba1\u67e5\u7684\u5de5\u5177\uff0c\u627e\u5230\u4ee5\u4e0b\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x) = \\displaystyle\\frac{4x^3 + 6x^2 -2x + 1}{x^2-4}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf \u6458\u8981\uff1a \u672c\u8bfe\u4ecb\u7ecd\u4e86\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6982\u5ff5\uff0c\u5e76\u5c06\u8fd9\u4e9b\u6982\u5ff5\u5e94\u7528\u4e8e\u4ee3\u6570\u51fd\u6570\u7684\u5b9e\u9645\u4f8b\u5b50\u4e2d\u3002\u6211\u4eec\u5c06\u5ba1\u67e5\u7528\u4e8e\u786e\u5b9a\u8fd9\u4e9b\u5143\u7d20\u7684\u56fe\u5f62\u548c\u5206\u6790\u6280\u672f\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f \u6b63\u786e\u5b9a\u4e49\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u3002 \u5e94\u7528\u56fe\u5f62\u65b9\u6cd5\u6765\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u548c\u503c\u57df\u3002 \u6784\u5efa\u7b26\u53f7\u8868\u6765\u5206\u6790\u51fd\u6570\u7684\u884c\u4e3a\u3002 \u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u5b9a\u4e49 \u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u5bf9\u7ebf\u6027\u51fd\u6570\u3001\u4e8c\u6b21\u51fd\u6570\u53ca\u5176\u7c7b\u4f3c\u51fd\u6570\u8fdb\u884c\u4e86\u76f8\u5f53\u8be6\u7ec6\u7684\u7814\u7a76\u3002\u6211\u4eec\u8fd8\u7814\u7a76\u4e86\u76f4\u7ebf\u3001\u629b\u7269\u7ebf\u3001\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u7b49\u66f2\u7ebf\uff0c\u4ee5\u53ca\u591a\u9879\u5f0f\u548c\u4e00\u822c\u4ee3\u6570\u51fd\u6570\u7684\u64cd\u4f5c\u3002\u5b8c\u6210\u8fd9\u4e9b\u5185\u5bb9\u540e\uff0c\u73b0\u5728\u66f4\u5bb9\u6613\u6df1\u5165\u7406\u89e3\u5173\u4e8e\u51fd\u6570\u7684\u4e00\u4e9b\u66f4\u57fa\u7840\u7684\u65b9\u9762\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u8fd9\u6b21\u5c06\u8981\u5ba1\u67e5\u7684\u5185\u5bb9\uff0c\u9996\u5148\u5f15\u5165\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6982\u5ff5\u3002 \u8bbe \u4e3a\u4e00\u4e2a\u5b9a\u4e49\u5728\u96c6\u5408 \u548c \u4e4b\u95f4\u7684\u51fd\u6570 \u96c6\u5408 \u548c \u5206\u522b\u79f0\u4e3a\u201c\u8f93\u5165\u96c6\u201d\u548c\u201c\u8f93\u51fa\u96c6\u201d\u3002\u57fa\u4e8e\u8fd9\u4e9b\u96c6\u5408\uff0c\u5b9a\u4e49\u4e86\u4ee5\u4e0b\u96c6\u5408\uff1a \u793a\u4f8b\u5206\u6790 \u867d\u7136\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6982\u5ff5\u672c\u8d28\u4e0a\u662f\u7406\u8bba\u95ee\u9898\uff0c\u4f46\u5b83\u4eec\u7684\u7406\u89e3\u66f4\u591a\u4f9d\u8d56\u4e8e\u5b9e\u9645\u4f8b\u5b50\u7684\u5e94\u7528\u3002\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u5206\u6790\u4ee5\u4e0b\u4e09\u4e2a\u6848\u4f8b\u6765\u5c55\u793a\u8fd9\u4e9b\u6982\u5ff5\u7684\u5e94\u7528\uff1a \u8ba1\u7b97\uff1a \u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf \u8ba9\u6211\u4eec\u5f00\u59cb\u5206\u6790 \u5199\u51fa \u3002\u5982\u679c\u6211\u4eec\u8fd9\u6837\u505a\uff0c\u5c31\u4f1a\u5f97\u5230\u4ee5\u4e0b\u65b9\u7a0b 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