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 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 53: 11



Work Step by Step

For functions $f$ and $g$, $(f.g)(x)=f(x).g(x)$ Thus, $(f.g)(x)$ is only defined for $x$-values for which both $f(x)$ and $g(x)$ are both defined. This means that domain of $(f.g)(x)$ consists of the numbers $x$ that are in the domains of both $f$ and $g$. Hence, the given statement is $\text{true}$.
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