Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 279: 17


(a) $\dfrac{1}{17}$ (b) $\dfrac{1}{5}$ (c) $1$ (d) $\dfrac{1}{2}$

Work Step by Step

(a) $(f\circ g)(4)= f(g(4))=f\left(\dfrac{1}{4^{2}+1}\right)=f\left(\dfrac{1}{17}\right)=\left|\dfrac{1}{17}\right|=\dfrac{1}{17}$ (b) $(g\circ f)(2)=g(f(2))=g(|2|)=g(2)=\dfrac{1}{2^{2}+1}=\dfrac{1}{5}$ (c) $(f\circ f)(1)=f(f(1))=f(|1|)=f(1)=|1|=1$ (d) $(g\circ g)(0)=g(g(0))=g\left(\dfrac{1}{0^{2}+1}\right)=g(1)=\dfrac{1}{1^{2}+1}=\dfrac{1}{2}$
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