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  4. If f: R arrow R is a function given by f(x)=2x-2-x, then f-1((3/2)) equals

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Q. If $f: R \rightarrow R$ is a function given by $f(x)=2^x-2^{-x}$, then $f^{-1}\left(\frac{3}{2}\right)$ equals

Relations and Functions - Part 2

Solution:

$2^x-2^{-x}=\frac{3}{2} \Rightarrow 2^x-\frac{1}{2^x}=\frac{3}{2}$
$ \Rightarrow 2 \cdot 2^{2 x}-3 \cdot 2^x-2=0$
$\left(2^x-2\right)\left(2 \cdot 2^x+1\right)=0 $
$2^x=2 \Rightarrow x=1 $