Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 50

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

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