Question

find the range of the function f(x)= 2+x/2-x. please don't spam...spammed answers are reported.....I nead a clear answer with good explanation..​

Answer 1

Step-by-step explanation:

Range of function : The range of the function f(x) is defined as the set of all output values .

$\sf Let \: y = \frac{2+x}{2-x} \\ \\ \sf To\:find\:range\:covert\:the\:given\: function \: in \: terms \:of y \\ \\ \sf \longrightarrow y(2-x) = 2+x \\ \\ \sf \longrightarrow 2y - xy = 2 + x \\ \\ \sf \longrightarrow 2y - 2 = x + xy \\ \\ \sf \longrightarrow 2(y-1) = x(1+y) \\ \\ \sf \longrightarrow x = \frac{2(y-1)}{1+y} \\ \\ \sf Now\:the\:set\:of\: values\: of \: y \: gives\:us \: range \\ \\ \sf y = R - (-1) \\ \\ \sf So \: range \: of \: given \: function \: is \: R - (-1) \\ \\ \sf Where \: R \: is \: set \: of \: all \: real \: numbers$

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