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 228: 17

Answer

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Work Step by Step

We are given the functions: $f(x)=\dfrac{x^3}{4}$ $g(x)=\sqrt[3]{4x}$ Compute $f\circ g$ and $g\circ f$: $(f\circ g)(x)=f(g(x))=f\left(\sqrt[3]{4x}\right)=\dfrac{(\sqrt[3]{4x})^3}{4}=\dfrac{4x}{4}=x$ $(g\circ f)(x)=g(f(x))=g\left(\dfrac{x^3}{4}\right)=\sqrt[3]{4\left(\dfrac{x^3}{4}\right)}=\sqrt[3]{x^3}=x$ We got: $(f\circ g)(x)=(g\circ f)(x)=x$, therefore $f$ and $g$ are inverse functions.
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