Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 51

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

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