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: 77



Work Step by Step

If for a function $f(x)=y$ then for the inverse function $f^{-1}(y)=x.$ Since $f$ is one-to-one then for each $x$ there is a unique $f(x)$ and all the $f(x)$ values are distinct. Hence if $f(x)=y$, then $f^{−1}(y)=x$. With $f(7)=13$, then $f^{−1}(13)=7.$
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