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: 18


(a) $\dfrac{11}{6}$ (b) $\dfrac{3}{2}$ (c) $1$ (d) $\dfrac{12}{17}$

Work Step by Step

(a) $(f\circ g)(4)= f(g(4))=f\left(\dfrac{3}{4^{2}+2}\right)=f\left(\dfrac{1}{6}\right)=\left|\dfrac{1}{6}-2\right|=\left|-\dfrac{11}{6}\right|=\dfrac{11}{6}$ (b) $(g\circ f)(2)=g(f(2))=g(|2-2|)=g(0)=\dfrac{3}{0^{2}+2}=\dfrac{3}{2}$ (c) $(f\circ f)(1)=f(f(1))=f(|1-2|)=f(1)=|1-2|=1$ (d) $(g\circ g)(0)=g(g(0))=g\left(\dfrac{3}{0^{2}+2}\right)=g\left(\dfrac{3}{2}\right)=\dfrac{3}{\left(\frac{3}{2}\right)^{2}+2}=\dfrac{3}{\frac{9}{4}+\frac{8}{4}}=\dfrac{3}{\frac{17}{4}}=3 \cdot \dfrac{4}{17}=\dfrac{12}{17}$
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