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: 32

Answer

a) $3x^4$ b) $81x^4$ c) $x^{16}$

Work Step by Step

We are given the functions: $f(x)=3x$ $g(x)=x^4$ a) Find $f\circ g$: $(f\circ g)(x)=f(g(x))=f(x^4)=3(x^4)=3x^4$ b) Find $g\circ f$: $(g\circ f)(x)=g(f(x))=g(3x)=(3x)^4=81x^4$ c) Find $g\circ g$: $(g\circ g)(x)=g(g(x))=g(x^4)=(x^4)^4=x^{16}$
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