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: 37

Answer

a) $x^2$; domain $(-\infty,\infty)$ b) $x^2$; domain: $(-\infty,\infty)$

Work Step by Step

We are given the functions: $f(x)=x^3$ $g(x)=x^{2/3}$ Determine the domains $D_f$ and $D_g$ of the two functions: $D_f=(-\infty,\infty)$ $D_g=(-\infty,\infty)$ a) Find $f\circ g$ and its domain $D_{f\circ g}$: $(f\circ g)(x)=f(g(x))=f\left(x^{2/3}\right)=(x^{2/3})^3=x^2$ $D_{f\circ g}=(-\infty,\infty)$ b) Find $g\circ f$ and its domain $D_{g\circ f}$: $(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^{2/3}=x^2$ $D_{g\circ f}=(-\infty,\infty)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.