Answer
$\text{False}$
Work Step by Step
Let $f(x)=x$ and $g(x)=\dfrac{1}{x}$.
Then,
$f(x).g(x)=x × \dfrac{1}{x}=1 $
$f(g(x))=f(\frac{1}{x})=\dfrac{1}{x}$
From above example, $f(g(x))\ne f(x).g(x)$.
Hence, the given statement is false.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
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 279: 5
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