Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 73

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

$f(x)=\frac{x^2-4}{2x^2},$ $y=\frac{x^2-4}{2x^2},$ a. $x=\frac{y^2-4}{2y^2},$ $2y^2x=y^2-4,$ $2y^2x-y^2=-4,$ $y^2(2x-1)=-4,$ $y^2=\frac{2}{\sqrt{1-2x}},$ $y=\frac{2}{\sqrt{1-2x}}=f^{-1}(x)$ b. Domain of $f(x)$ is $x\in\mathbb{R} -\{ 0\}$ and Domain of $f^{-1}(x)$ is $x < 1/2$