Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 58

$f^{-1}(x)=-\frac{3}{x} $ See graph.

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