Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.2 - Inverse Functions - Practice - Page 848: 9

Answer

$f^{-1}(x)=\frac{x-3}{2}$ The graphs of $f$ (blue line) and $f^{-1}$ (red line) are shown in the following image:

Work Step by Step

Equation given: $f(x)=2x+3$ Replace $f(x)$ with $y$: $y=2x+3$ Make $x$ the subject: $\frac{y-3}{2}=x$ Interchange $y$ with $x$: $y=\frac{x-3}{2}$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=\frac{x-3}{2}$ Graph $f$ and $f^{-1}$ using technology or by making a table of ordered pairs for each line and joining the points found.
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