Answer
$f^{-1}(x)=2-\frac{4}{x}$
Work Step by Step
$f(x)=\frac{4}{2-x},$
$y=\frac{4}{2-x},$
a. $x=\frac{4}{2-y},$
$2-y=\frac{4}{x},$
$y=2-\frac{4}{x}=f^{-1}(x),$
b. Domain of $f(x)$ is $x\in \mathbb{R} \ne 2$
and Domain of $f^{-1}(x)$ is $x\in \mathbb{R} \ne 0,$
