Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 67

$f^{-1}(x)=\frac{x}{3x-2}$

$f(x)=\frac{2x}{3x-1},$ $y=\frac{2x}{3x-1},$ a. $x=\frac{2y}{3y-1},$ $x(3y-1)=2y,$ $3xy-x=2y,$ $3xy-2y=x,$ $y(3x-2)=x,$ $y=\frac{x}{3x-2}=f^{-1}(x),$ b.Domain of $f(x)$ is $x\in \mathbb{R} \ne \frac{1}{3},$ and Domain of $f^{-1}(x)$ is $x\in \mathbb{R} \ne \frac{2}{3}$