Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 61

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

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