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 - Chapter Test - Page 372: 1


(a) $ \frac{2x+7}{2x+3}$, $\{x|x\ne-\frac{3}{2} \}$. (b) $ 5$. (c) $ -3$.

Work Step by Step

Given $f(x)=\frac{x+2}{x-2}$ and $g(x)=2x+5$, we have: (a) $(f\circ g)(x)=\frac{(2x+5)+2}{(2x+5)-2}=\frac{2x+7}{2x+3}$ with domain $\{x|x\ne-\frac{3}{2} \}$. (b) $(g\circ f)(-2)=g(\frac{-2+2}{-2-2})=g(0)=5$. (c) $(f\circ g)(-2)=\frac{2(-2)+7}{2(-2)+3}=-3$.
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