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: 33


a) $x$ b) $x$ c) $x^9+3x^6+3x^3+2$

Work Step by Step

We are given the functions: $f(x)=\sqrt[3]{x-1}$ $g(x)=x^3+1$ a) Find $f\circ g$: $(f\circ g)(x)=f(g(x))=f(x^3+1)=\sqrt[3]{x^3+1-1}=\sqrt[3]{x^3}=x$ b) Find $g\circ f$: $(g\circ f)(x)=g(f(x))=g(\sqrt[3]{x-1})=(\sqrt[3]{x-1})^3+1=x-1+1=x$ c) Find $g\circ g$: $(g\circ g)(x)=g(g(x))=g(x^3+1)=(x^3+1)^3+1=x^9+3x^6+3x^3+2$
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