{"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":"<h2>Solution :<\/h2>\n<p>we have,\u00a0 f(x) = \\(x-2\\over 3-x\\)<\/p>\n<p>Domain of f : Clearly f(x) is defined for all x satisfying 3 &#8211; x \\(\\ne\\) 0 i.e. x \\(\\ne\\) 3<\/p>\n<p>Hence, Domain of f is R &#8211; {3}<\/p>\n<p>Range of f : Let y = f(x), i.e.\u00a0 y = \\(x-2\\over 3-x\\)<\/p>\n<p>\\(\\implies\\) 3y &#8211; xy = x &#8211; 2<\/p>\n<p>= x(y + 1) = 3y + 2<\/p>\n<p>\\(\\implies\\) x = \\(3y + 2\\over y + 1\\)<\/p>\n<p>Clearly, x assumes real values for all y expect y + 1 = 0 i.e. y = -1<\/p>\n<p>Hence, Range of f is R &#8211; {-1}<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-y-2x-3-y-3x-2-5-then-find-x-y-where-denotes-greatest-integer-function\/\" aria-label=\"\u201cIf y = 2[x] + 3 &amp; y = 3[x \u2013 2] + 5, then find [x + y] where [.] denotes greatest integer function.\u201d (Edit)\">If y = 2[x] + 3 &amp; y = 3[x \u2013 2] + 5, then find [x + y] where [.] denotes greatest integer function.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-domain-of-the-function-fx-1over-x-2\/\" aria-label=\"\u201cFind the domain of the function f(x) = \\(1\\over x + 2\\).\u201d (Edit)\">Find the domain of the function f(x) = \\(1\\over x + 2\\).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-period-of-the-function-fx-ex-xcospi-xcos2pi-x-cosnpi-x\/\" aria-label=\"\u201cFind the period of the function f(x) = \\(e^{x-[x]+|cos\\pi x|+|cos2\\pi x|+ \u2026.. + |cosn\\pi x|}\\)\u201d (Edit)\">Find the period of the function f(x) = \\(e^{x-[x]+|cos\\pi x|+|cos2\\pi x|+ \u2026.. + |cosn\\pi x|}\\)<\/a><\/p>\n<p><a class=\"row-title\" style=\"color: #2271b1; text-decoration: none; cursor: pointer; transition: none 0s ease 0s; outline: 0px; overflow-wrap: break-word; font-weight: 600; font-size: 14px; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #f6f7f7;\" href=\"https:\/\/mathemerize.com\/find-the-inverse-of-the-function-fx-log_ax-sqrtx21-a-1-and-assuming-it-to-be-an-onto-function\/\" aria-label=\"\u201cFind the inverse of the function f(x) = \\(log_a(x + \\sqrt{(x^2+1)})\\); a &gt; 1 and assuming it to be an onto function.\u201d (Edit)\">Find the inverse of the function f(x) = \\(log_a(x + \\sqrt{(x^2+1)})\\); a &gt; 1 and assuming it to be an onto function.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-range-of-the-function-log_sqrt22-log_216sin2x1\/\" aria-label=\"\u201cFind the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)\u201d (Edit)\">Find the range of the function \\(log_{\\sqrt{2}}(2-log_2(16sin^2x+1))\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : we have,\u00a0 f(x) = \\(x-2\\over 3-x\\) Domain of f : Clearly f(x) is defined for all x satisfying 3 &#8211; x \\(\\ne\\) 0 i.e. x \\(\\ne\\) 3 Hence, Domain of f is R &#8211; {3} Range of f : Let y = f(x), i.e.\u00a0 y = \\(x-2\\over 3-x\\) \\(\\implies\\) 3y &#8211; xy = &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-the-domain-and-range-of-function-fx-x-2over-3-x\/\"> <span class=\"screen-reader-text\">Find the domain and range of function f(x) = \\(x-2\\over 3-x\\).<\/span> Read More &raquo;<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find 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 &#8211; 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