Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 258: 24


$(-\infty, 14]$

Work Step by Step

The radicand (expression inside a radical sign) of a square root cannot be negative as its root is an imaginary number. This means that the radicand, which is $84-6x$, must be greater than or equal to 0. Thus, $84-6x\ge 0 \\-6x \ge 0-84 \\-6x \ge -84$ Divide both sides by $-6$. Note that since a negative number is being divided on both sides of an inequality, the inequality sign flips to the opposite direction. $\dfrac{-6x}{-6} \le \dfrac{-84}{-6} \\x \le 14$ Therefore, the domain of the given function is $(-\infty, 14]$.
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