Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 60

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

Step 1. $f(x)=\frac{4}{x+2} \Longrightarrow y=\frac{4}{x+2} \Longrightarrow x=\frac{4}{y+2} \Longrightarrow y=\frac{4}{x}-2 \Longrightarrow f^{-1}(x)=\frac{4}{x}-2$ Step 2. Check $f(f^{-1}(x))=\frac{4}{(\frac{4}{x}-2)+2}=x$ and $f^{-1}(f(x))=\frac{4}{\frac{4}{x+2}}-2=x$ Step 3. See graph.