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: 42

Answer

(a) $ \sqrt {-2x-1}$, domain $\{x|x\le-\frac{1}{2} \}$. (b) $ 1-2\sqrt {x-2}$, domain $\{x|x\ge2 \}$. (c) $ \sqrt {\sqrt {x-2}-2}$, domain $\{x|x\ge6 \}$. (d) $ 4x-1$, domain $\{x|x=all\ real\ numbers \}$.

Work Step by Step

Given $f(x)=\sqrt {x-2}$ and $g(x)=1-2x$, we have: (a) $f\circ g=\sqrt {(1-2x)-2}=\sqrt {-2x-1}$, domain $\{x|x\le-\frac{1}{2} \}$. (b) $g\circ f=1-2\sqrt {x-2}$, domain $\{x|x\ge2 \}$. (c) $f\circ f=\sqrt {\sqrt {x-2}-2}$, domain $\{x|x\ge6 \}$. (d) $g\circ g=1-2(1-2x)=4x-1$, domain $\{x|x=all\ real\ numbers \}$.
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