Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 230: 98


$f$ and $f^{-1}$ are inverses.

Work Step by Step

We are given the functions: $f(x)=x+2$ $f^{-1}(x)=x-2$ Compute $f(f^{-1}(x))$ for $x\in\{-10,0,7,45\}$: $f(f^{-1}(-10))=f(-12)=-10$ $f(f^{-1}(0))=f(-2)=0$ $f(f^{-1}(7))=f(5)=7$ $f(f^{-1}(45))=f(43)=45$ Compute $f^{-1}(f(x))$ for $x\in\{-10,0,7,45\}$: $f^{-1}(f(-10))=f^{-1}(-8)=-10$ $f^{-1}(f(0))=f^{-1}(2)=0$ $f^{-1}(f(7))=f^{-1}(9)=7$ $f^{-1}(f(45))=f^{-1}(47)=45$ Put the data in a table. We notice that we have: $f(f^{-1}(x))=f^{-1}(f(x))=x$ This means the two functions are inverses of each other.
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