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: 84


also decreasing on $(0,5)$.

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 the domain of $f$ is the range of $f^{-1}$ and the range of $f$ is the domain of $f^{-1}$. Hence if $f$ is decreasing on $(0,5)$, it means that for $a\lt b$, $f(a)\gt f(b)$. Hence for $f^{-1}$ if $f(a)\gt f(b)$, then $f^{-1}f(a)=a\lt b=f^{-1}f(b)$, hence it is also decreasing on $(0,5)$.
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