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