Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.6 - Combinations of Functions: Composite Functions - 2.6 Exercises - Page 219: 38


a) $x^{5/4}$; domain $[0,\infty)$ b) $x^{5/4}$; domain: $[0,\infty)$

Work Step by Step

We are given the functions: $f(x)=x^5$ $g(x)=\sqrt [4]x=x^{1/4}$ Determine the domains $D_f$ and $D_g$ of the two functions: $D_f=(-\infty,\infty)$ $D_g=[0,\infty)$ a) Find $f\circ g$ and its domain $D_{f\circ g}$: $(f\circ g)(x)=f(g(x))=f\left(x^{1/4}\right)^5=x^{5/4}$ $D_{f\circ g}=[0,\infty)$ b) Find $g\circ f$ and its domain $D_{g\circ f}$: $(g\circ f)(x)=g(f(x))=g(x^5)=(x^5)^{1/4}=x^{5/4}$ $D_{g\circ f}=[0,\infty)$
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