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 280: 37


(a) $ \frac{3x}{2-x}$, domain $\{x|x\ne0,2 \}$. (b) $ \frac{2x-2}{3}$, domain $\{x|x\ne1 \}$. (c) $ \frac{3x-3}{4-x}$, domain $\{x|x\ne1,4 \}$. (d) $ x$, domain $\{x|x\ne0 \}$.

Work Step by Step

Given $f(x)=\frac{3}{x-1}$ and $g(x)=\frac{2}{x}$, we have: (a) $f\circ g=\frac{3}{(\frac{2}{x})-1}=\frac{3x}{2-x}$, domain $\{x|x\ne0,2 \}$. (b) $g\circ f=\frac{2}{\frac{3}{x-1}}=\frac{2x-2}{3}$, domain $\{x|x\ne1 \}$. (c) $f\circ f=\frac{3}{(\frac{3}{x-1})-1}=\frac{3x-3}{4-x}$, domain $\{x|x\ne1,4 \}$. (d) $g\circ g=\frac{2}{\frac{2}{x}}=x$, domain $\{x|x\ne0 \}$.
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