The range of the function f ( x ) = 2 − x 2 + x , x  = 2 is

y = 2 − x 2 + x ⇒ 2 y − y x = 2 + x ⇒ x ( y + 1 ) = 2 y − 2 ⇒ x = y + 1 2 y − 2 ⇒ f − 1 ( x ) = x + 1 2 x − 2 ∴ Range = f = Domain f − 1 = R − { − 1 }

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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsDomain-RangeEasy2 minQB

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The range of the function $f (x) = \frac{2 + x}{2 - x}, x \neq = 2$ is

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$y = \frac{2 + x}{2 - x} \Rightarrow 2 y - y x = 2 + x \Rightarrow x (y + 1) = 2 y - 2 \Rightarrow x = \frac{2 y - 2}{y + 1} \Rightarrow f^{- 1} (x) = \frac{2 x - 2}{x + 1}$ $∴ Range = f = Domain f^{- 1} = R - {- 1}$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Domain-Range

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