Answer
$f(g(x))$ is continuous for all values of $x.$
Work Step by Step
Using Theorem $1.12:$
Since $g(x)$ is continuous for any value of $x$, and $f(x)$ is continuous for any value of $x\to f(g(x))$ is continuous for all values of x.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 1 - Limits and Their Properties - 1.4 Exercises - Page 80: 67
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