Question

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

• A. $\frac{-1}{2}$
• B. 1
• C. 2
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

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