{"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). 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