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: 52



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{Odd\:Function:}\:\: $ A function is odd if $\ g(-x)=-g(x)\ $ for all $\ x\in \mathbb{R}. $ $g(x)=x^4+3x^2-1$ $g(-x)=(-x)^4+3(-x)^2-1$ $g(-x)=x^4+3x^2-1$ Now, $-g(x)=-(x^4+3x^2-1)=-x^4-3x^2+1$ Since, $g(-x)=g(x)\mathrm{,\:therefore\:}x^4+3x^2-1\mathrm{\:is\:an\:even\:function}$ $g(-x)\ne-g(x)\mathrm{,\:therefore\:}x^4+3x^2-1\mathrm{\:is\:not\:an\:odd\:function}$
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