## Precalculus (6th Edition) Blitzer

$(-\infty, 14]$
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 $(-\infty, 14]$.