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: 54



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}. $ $g(x)=\frac{x}{x^2-1}$ $g(-x)=\frac{-x}{(-x)^2-1}$ $g(-x)=\frac{-x}{x^2-1}$ $g(-x)=-\frac{x}{x^2-1}$ Now, $-g(x)=-\frac{x}{x^2-1}$ Since, $g(-x)\ne g(x)\mathrm{,\:therefore\:}\frac{x}{x^2-1}\mathrm{\:is\:not\:an\:even\:function}$ $g(-x)=-g(x)\mathrm{,\:therefore\:}\frac{x}{x^2-1}\mathrm{\:is\:an\:odd\:function}$
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