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: 50


$\mathrm{Neither\:even\:nor\:odd}.$ $\:$ $ $

Work Step by Step

$\mathrm{Function\:Parity\:Definition:}$ $\mathrm{Even\:Function:}\:\:$ A function is even if $\ f(-x)=f(x)\ $ for all $\ x\in \mathbb{R}.$ $\mathrm{Odd\:Function:}\:\:$ A function is odd if $\ f(-x)=-f(x)\ $ for all $\ x\in \mathbb{R}.$ $f(x)=x^2+x$ $f(-x)=(-x)^2-x=x^2-x$ Now, $-f(x)=-(x^2+x)=-x^2-x$ Since, $f(-x)\ne f(x)\mathrm{,\:therefore\:}x^2+x\mathrm{\:is\:not\:an\:even\:function}$ $f(-x)\ne -f(x)\mathrm{,\:therefore\:}x^2+x\mathrm{\:is\:not\:an\:odd\:function}$
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