Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.2 One-to-One Functions; Inverse Functions - 5.2 Assess Your Understanding - Page 267: 78



Work Step by Step

If for a function $g(x)=y$ then for the inverse function $g^{-1}(y)=x.$ Since $g$ is one-to-one then for each $x$ there is a unique $g(x)$ and all the $g(x)$ values are distinct. Hence, if $g(x)=y$, then $g^{−1}(y)=x$. Thus, if $g(-5)=3$, then $g^{−1}(3)=-5$
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