University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 51



Work Step by Step

$\mathrm{Function\:Parity\:Definition:}$ $\mathrm{Even\:Function:}\:\:$ A function is even if $\ g(-x)=g(x)\ $ for all $\ x\in \mathbb{R}.$ $\mathrm{Even\:Function:}\:\:$ A function is odd if $\ g(-x)=-g(x)\ $ for all $\ x\in \mathbb{R}.$ $g(x)=x^3+x$ $g(-x)=(-x)^3-x=-x^3-x$ Now, $-g(x)=-(x^3+x)=-x^3-x$ Since, $g(-x)\ne g(x)\mathrm{,\:therefore\:}x^3+x\mathrm{\:is\:not\:an\:even\:function}$ $g(-x)=-g(x)\mathrm{,\:therefore\:}x^3+x\mathrm{\:is\:an\:odd\:function}$
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