Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Additional and Advanced Exercises - Page 38: 1


Yes, see explanations.

Work Step by Step

Yes, let $f(x)$ be a one-to-one function and we can find its inverse as $g(x)=f^{-1}(x)$. Using the properties of inverse functions, we have $f(g(x))=f(f^{-1}(x))=x$ and $g(f(x))=f^{-1}(f(x))=x$, thus $f(g(x))=g(f(x))$.
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