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: 55



Work Step by Step

$\mathrm{Function\:Parity\:Definition:} $ $\mathrm{Even\:Function:}\:\: $ A function is even if $\ h(-t)=h(t)\ $ for all $\ x\in \mathbb{R}. $ $\mathrm{Odd\:Function:}\:\: $ A function is odd if $\ h(-t)=-h(t)\ $ for all $\ x\in \mathbb{R}. $ $h(t)=\frac{1}{t-1}$ $h(-t)=\frac{1}{-t-1}$ Now, $-h(t)=-\frac{1}{t-1}$ Since, $h(-t)\ne h(t)\mathrm{,\:therefore\:}\frac{1}{t-1}\mathrm{\:is\:not\:an\:even\:function}$ $h(-t)\ne -h(t)\mathrm{,\:therefore\:}\frac{1}{t-1}\mathrm{\:is\:not\:an\:odd\:function}$
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