Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 62

$f^{-1}(x)=2-\frac{4}{x}$

Step 1. $f(x)=\frac{4}{2-x} \Longrightarrow y=\frac{4}{2-x} \Longrightarrow x=\frac{4}{2-y} \Longrightarrow y=2-\frac{4}{x} \Longrightarrow f^{-1}(x)=2-\frac{4}{x}$ Step 2. Check $f(f^{-1}(x))=\frac{4}{2-(2-\frac{4}{x})}=x$ and $f^{-1}(f(x))=2-\frac{4}{\frac{4}{2-x}}=x$