Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - Exercises - Page 157: 64

Answer

$(-\infty, -2] \cup [2, +\infty)$

Work Step by Step

The elementary radical function $y=\sqrt{x}$ is defined only when the radicand, which is $x$, is greater than or equal to 0. This means that the given function $g(x)=\sqrt{x^2-4}$ is defined only when $x^2-4\ge 0$. Solve the inequality to have: $(x-2)(x+2) \ge 0$ Note that the value of $g$ is greater than or equal to $0$ when: $x \ge 2$ or when $x \le -2$ The given function is defined when $x \ge 2$ or when $x \le -2$. Therefore the domain of the given function is: $(-\infty, -2] \cup [2, +\infty)$
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