Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.8 Function Operations and Composition - 2.8 Exercises - Page 289: 85

Answer

(a) $\sqrt {\frac{1}{x+5}}$, domain: $(-5,\infty)$ (b) $\frac{1}{\sqrt x+5}$, domain: $[0,\infty)$

Work Step by Step

(a) Given $f(x)=\sqrt {x}, x\ge0$ and $g(x)=\frac{1}{x+5}, x\ne-5$, we have $(f\circ g)(x)=f(g(x))=\sqrt {\frac{1}{x+5}}$. From $x+5\gt0$, we have $x\gt-5$. Combine all the conditions, we can find its domain: $(-5,\infty)$ (b) $(g\circ f)(x)=g(f(x))=\frac{1}{\sqrt x+5}$. Combine all the conditions, we can find its domain: $[0,\infty)$
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