## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 258: 67

#### Answer

a. $\frac{2x}{3x+1}$ b. $(-\infty,-\frac{1}{3})\cup(-\frac{1}{3},0)\cup(0,\infty)$

#### Work Step by Step

Given $f(x)=\frac{2}{x+3}, x\ne-3$ and $g(x)=\frac{1}{x}, x\ne0$, we have: a. $(f\circ g)(x)=\frac{2}{1/x+3}=\frac{2x}{3x+1}$ b. The domain of the above function can be found as $\{x|x\ne-\frac{1}{3},0\}$ or $(-\infty,-\frac{1}{3})\cup(-\frac{1}{3},0)\cup(0,\infty)$ (note that $x=-3$ is in the domain)

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