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 229: 85



Work Step by Step

$f(x)=x+4$ $y=x+4~~$ (Interchange $x$ and $y$): $x=y+4$ $y=x-4$ $f^{-1}(x)=x-4$ $g(x)=2x-5$ $y=2x-5~~$ (Interchange $x$ and $y$): $x=2y-5$ $x+5=2y$ $y=\frac{1}{2}x+\frac{5}{2}$ $g^{-1}(x)=\frac{1}{2}x+\frac{5}{2}$ $g^{-1}~o~f^{-1}=g^{-1}(f^{-1})=g^{-1}(x-4)=\frac{1}{2}(x-4)+\frac{5}{2}=\frac{1}{2}x-2+\frac{5}{2}=\frac{1}{2}x+\frac{1}{2}$
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