{"id":18075,"date":"2022-11-28T10:00:44","date_gmt":"2022-11-28T04:30:44","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=18075"},"modified":"2022-11-29T18:01:53","modified_gmt":"2022-11-29T12:31:53","slug":"domain-co-domain-range-function","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/domain-co-domain-range-function\/","title":{"rendered":"Domain, co-domain and range of function"},"content":{"rendered":"<h2>Domain, co-domain and range of function<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/FdK9_Fp76cw?feature=oembed\" frameborder=\"0\" gesture=\"media\" allow=\"encrypted-media\" allowfullscreen><\/iframe><\/p>\n<p>If a function f is defined from a set A to set B then for f : A\u00a0\u27f6 B\u00a0set A is called the domain of function f and set B is called the co-domain of function f. The set of all f-images of the elements of A is called the range of function f.<br \/>\nIn other words, we can say<br \/>\nDomain = All possible values of x for which f(x) exists.<br \/>\nRange = For all values of x, all possible values of f(x).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/c1.staticflickr.com\/5\/4167\/34476908061_bb0f24c9aa_o.jpg\" alt=\"function-3\" width=\"453\" height=\"320\" \/><\/p>\n<h3>Methods for finding domain and range of function<\/h3>\n<p><strong>(i) Domain<\/strong><br \/>\nExpression under even root (i.e., square root, fourth root etc.) \u2265 0. Denominator \u2260 0.<br \/>\nIf domain of y = f(x) and y = g(x) are D<sub>1<\/sub> and D<sub>2<\/sub> respectively then the domain of f(x) \u00b1 g(x) or f(x) . g(x) is D<sub>1 <\/sub>\u2229 D<sub>2<\/sub>.<br \/>\nWhile domain of \\(\\frac { f(x) }{ g(x) } \\) is D<sub>1 <\/sub>\u2229 D<sub>2<\/sub> \u2013 {g(x) = 0}.<br \/>\nDomain of (\u221af(x)) = D<sub>1 <\/sub>\u2229 {x : f(x) \u2265 0}<\/p>\n<p><strong>(ii) Range:<\/strong><br \/>\nRange of y = f(x) is collection of all outputs f(x) corresponding to each real number in the domain.<\/p>\n<ol>\n<li>If domain \u2208 finite number of points \u21d2 range \u2208 set of corresponding f(x) values.<\/li>\n<li>If domain \u2208 R or R \u2013 [some finite points]. Then express x in terms of y. From this find y for x to be defined (i.e., find the values of y for which x exists).<\/li>\n<li>If domain \u2208 a finite interval, find the least and greatest value for range using monotonicity.<\/li>\n<\/ol>\n<h3>Domain and Range of Some Standard Functions<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/5\/4158\/34611319455_4db31e80d1_o.jpg\" alt=\"function-4\" width=\"617\" height=\"608\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/c1.staticflickr.com\/5\/4170\/33801218083_97beef9aa2_o.jpg\" alt=\"function-5\" width=\"617\" height=\"564\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Domain, co-domain and range of function If a function f is defined from a set A to set B then for f : A\u00a0\u27f6 B\u00a0set A is called the domain of function f and set B is called the co-domain of function f. The set of all f-images of the elements of A is called [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[6802,6801,5217,6803,6804],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Domain, co-domain and range of function - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/domain-co-domain-range-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Domain, co-domain and range of function\" \/>\n<meta property=\"og:description\" content=\"Domain, co-domain and range of function If a function f is defined from a set A to set B then for f : A\u00a0\u27f6 B\u00a0set A is called the domain of function f and set B is called the co-domain of function f. 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