Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

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

Answer

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

Work Step by Step

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 $f^{-1}$.
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