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: 21


$\mathrm{Domain:}\ \ (-\infty ,-5)\cup (-5,-3]\cup [3,5)\cup (5,\infty )$

Work Step by Step

$\mathrm{Remember:}\ $ We can take square root only of the positive numbers, i.e $\ \ \sqrt{f(x)}\quad \Rightarrow \quad \:f(x)\ge 0$ For a rational function, to find the domain, take the denominator of it and compare it to zero. Exclude the points obtained from the domain as they will be undefined. Taking the first step, we have: $x^2-9\ge 0$ $\Rightarrow\ x\le \:-3\quad \mathrm{or}\quad \:x\ge \:3$ Now take the denominator and compare it to zero. $4-\sqrt{x^2-9}=0$ $\Rightarrow\ x^2-9=16$ $\Rightarrow\ x=5,\:\:x=-5$ $\mathrm{Domain:}\ \ (-\infty ,-5)\cup (-5,-3]\cup [3,5)\cup (5,\infty )$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.