Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 68: 83


The function $|g(x)|$ acts like the function $|x|$.

Work Step by Step

We are given: $f(x)=|g(x)|$ Rewrite the function: $f(x)=\begin{cases} -g(x),\text{ for }g(x)\leq 0\\ g(x),\text{ for }g(x)>0 \end{cases}$ Because $g(x)$ is continuous, $f(x)$ is continuous in the intervals for which $g(x)\not=0$. In the points in which $g(x)=0$, $f(x)$ is also continuous due to the continuity of $g(x)$. Therefore the function $f$ is continuous on the domain of $g(x)$.
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