Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 258: 68

Answer

a. $\frac{5x}{4x+1}$ b. $(-\infty,-\frac{1}{4})\cup(-\frac{1}{4},0)\cup(0,\infty)$

Work Step by Step

Given $f(x)=\frac{5}{x+4}, x\ne-4$ and $g(x)=\frac{1}{x}, x\ne0$, we have: a. $(f\circ g)(x)=\frac{5}{1/x+4}=\frac{5x}{4x+1}$ b. The domain of the above function can be found as $\{x|x\ne-\frac{1}{4},0\}$ or $(-\infty,-\frac{1}{4})\cup(-\frac{1}{4},0)\cup(0,\infty)$ (note that $x=-4$ is in the domain)
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