Answer
$f^{-1}(x)=\frac{2}{3x}+\frac{5}{3}$
Work Step by Step
$f(x)=\frac{2}{3x-5},$
$y=\frac{2}{3x-5},$
$Domain =\{x|x \in \mathbb{R}, x\ne \frac{5}{3}\}$
$Range=\{y|y \in \mathbb{R},y\ne0 \}$
$x=\frac{2}{3y-5},$
$3y-5=\frac{2}{x},$
$3y=\frac{2}{x}+5,$
$y=\frac{2}{3x}+\frac{5}{3}=f^{-1}(x)$
$Domain=\{x|x \in \mathbb{R},x \ne 0\}$
$Range=\{y|y \in \mathbb{R}, y \ne \frac{5}{3}\}$
