Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 66

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

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