Aspire Faculty ID #18300 · Topic: AMU MCA 2017 · Just now
AMU MCA 2017

The range of the function $f(x)=\frac{2+x}{2-x},\ x\ne2$ is

Solution

Let $ y=\frac{2+x}{2-x} $ $ \Rightarrow 2y-xy=2+x $ $ \Rightarrow 2y-2=x+xy $ $ \Rightarrow 2y-2=x(1+y) $ $ \Rightarrow x=\frac{2y-2}{1+y} $ For real $x$, denominator $\neq0$ $ \Rightarrow 1+y\neq0 $ $ \Rightarrow y\neq-1 $ $ \therefore \text{Range}=R-{-1} $

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