Answer
Even
Work Step by Step
When $x\ge0,$
$f(x)=x|x|=x\times x=x^{2}$
$f(-x)=-x|-x|=-x\times x=-x^{2}$
$f(-x)=-f(x)$
When $x\lt0,$
$f(x)=x|x|=x\times-x=-x^{2}$
$f(-x)=-x|-x|=-x\times-x=x^{2}$
$f(-x)=-f(x)$
$\therefore f(x)$ is even.
Calculus: Early Transcendentals 9th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1337613924
ISBN 13:
978-1-33761-392-7
Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 21: 84
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