Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.1 Composite Functions - 5.1 Assess Your Understanding - Page 254: 21


a) $\dfrac{3}{\sqrt[3]4+1}$; b) $1$; c) $\dfrac{6}{5}$; d) $0$.

Work Step by Step

We are given the functions: $f(x)=\dfrac{3}{x+1}$ $g(x)=\sqrt[3] x$ a) $(f\circ g)(4)=f(g(4))=f\left(\sqrt[3] 4\right)=\dfrac{3}{\sqrt[3]4+1}$ b) $(g\circ f)(2)=g(f(2))=g\left(\dfrac{3}{2+1}\right)=g(1)=\sqrt[3] 1=1$ c) $(f\circ f)(1)=f(f(1))=f\left(\dfrac{3}{1+1}\right)=f\left(\dfrac{3}{2}\right)=\dfrac{3}{\dfrac{3}{2}+1}=\dfrac{6}{5}$ d) $(g\circ g)(0)=g(g(0))=g\left(\sqrt[3]0\right)=g\left(0\right)=\sqrt[3]0=0$
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