{"id":7176,"date":"2021-10-22T23:42:38","date_gmt":"2021-10-22T18:12:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7176"},"modified":"2021-10-24T23:54:41","modified_gmt":"2021-10-24T18:24:41","slug":"find-the-domain-and-range-of-function-fx-x-2over-3-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/","title":{"rendered":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\)."},"content":{"rendered":"

Solution :<\/h2>\n

we have,\u00a0 f(x) = \\(x-2\\over 3-x\\)<\/p>\n

Domain of f : Clearly f(x) is defined for all x satisfying 3 – x \\(\\ne\\) 0 i.e. x \\(\\ne\\) 3<\/p>\n

Hence, Domain of f is R – {3}<\/p>\n

Range of f : Let y = f(x), i.e.\u00a0 y = \\(x-2\\over 3-x\\)<\/p>\n

\\(\\implies\\) 3y – xy = x – 2<\/p>\n

= x(y + 1) = 3y + 2<\/p>\n

\\(\\implies\\) x = \\(3y + 2\\over y + 1\\)<\/p>\n

Clearly, x assumes real values for all y expect y + 1 = 0 i.e. y = -1<\/p>\n

Hence, Range of f is R – {-1}<\/p>\n


\n

Similar Questions<\/h3>\n

If y = 2[x] + 3 & y = 3[x \u2013 2] + 5, then find [x + y] where [.] denotes greatest integer function.<\/a><\/p>\n

Find the domain of the function f(x) = \\(1\\over x + 2\\).<\/a><\/p>\n

Find the period of the function f(x) = \\(e^{x-[x]+|cos\\pi x|+|cos2\\pi x|+ \u2026.. + |cosn\\pi x|}\\)<\/a><\/p>\n

Find the inverse of the function f(x) = \\(log_a(x + \\sqrt{(x^2+1)})\\); a > 1 and assuming it to be an onto function.<\/a><\/p>\n

Find the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : we have,\u00a0 f(x) = \\(x-2\\over 3-x\\) Domain of f : Clearly f(x) is defined for all x satisfying 3 – x \\(\\ne\\) 0 i.e. x \\(\\ne\\) 3 Hence, Domain of f is R – {3} Range of f : Let y = f(x), i.e.\u00a0 y = \\(x-2\\over 3-x\\) \\(\\implies\\) 3y – xy = …<\/p>\n

Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[50,43],"tags":[],"yoast_head":"\nFind the domain and range of function f(x) = \\(x-2\\over 3-x\\).<\/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:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : we have,\u00a0 f(x) = (x-2over 3-x) Domain of f : Clearly f(x) is defined for all x satisfying 3 – x (ne) 0 i.e. x (ne) 3 Hence, Domain of f is R – {3} Range of f : Let y = f(x), i.e.\u00a0 y = (x-2over 3-x) (implies) 3y – xy = … Find the domain and range of function f(x) = (x-2over 3-x). Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T18:12:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T18:24:41+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the domain and range of function f(x) = \\\\(x-2\\\\over 3-x\\\\).\",\"datePublished\":\"2021-10-22T18:12:38+00:00\",\"dateModified\":\"2021-10-24T18:24:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\"},\"wordCount\":176,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Function Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\",\"url\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\",\"name\":\"Find the domain and range of function f(x) = \\\\(x-2\\\\over 3-x\\\\).\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T18:12:38+00:00\",\"dateModified\":\"2021-10-24T18:24:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Find the domain and range of function f(x) = \\\\(x-2\\\\over 3-x\\\\).\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/","og_locale":"en_US","og_type":"article","og_title":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).","og_description":"Solution : we have,\u00a0 f(x) = (x-2over 3-x) Domain of f : Clearly f(x) is defined for all x satisfying 3 – x (ne) 0 i.e. x (ne) 3 Hence, Domain of f is R – {3} Range of f : Let y = f(x), i.e.\u00a0 y = (x-2over 3-x) (implies) 3y – xy = … Find the domain and range of function f(x) = (x-2over 3-x). Read More »","og_url":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T18:12:38+00:00","article_modified_time":"2021-10-24T18:24:41+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).","datePublished":"2021-10-22T18:12:38+00:00","dateModified":"2021-10-24T18:24:41+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/"},"wordCount":176,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Function Questions","Maths Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/","url":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/","name":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-22T18:12:38+00:00","dateModified":"2021-10-24T18:24:41+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Find the domain and range of function f(x) = \\(x-2\\over 3-x\\)."}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7176"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=7176"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7176\/revisions"}],"predecessor-version":[{"id":7268,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7176\/revisions\/7268"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}