Answer
$[-7, +\infty)$
Work Step by Step
The radicand (expression inside a radical) of a square root cannot be negative as its root is an imaginary number.
This means that the radicand, which is $5x+35$, must be greater than or equal to 0.
Thus,
$5x + 35\ge 0
\\5x \ge 0-35
\\5x \ge -35
\\x \ge \frac{-35}{5}
\\x \ge -7$
Therefore, the domain of the given function is $[-7, +\infty)$.
