Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises: 76

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.
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