#### Answer

$[3, +\infty)$

#### 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:
(1) The radicand of the first radical, which is $x-3$, must be greater than or equal to 0. Thus, $x$ can be any real number greater than or equal to $3$
(2) The radicand of the second radical, which is $x+4$, must be grater than or equal to 0. Thus, $x$ can be any real number greater than or equal to $-4$.
Based on (1) and (2) above, the restrictions to the value of $x$ are:
(1) $x \ge 3$; and
(2) $ x\ge -4$
Both of the restrictions above must be satisfied. Thus, the value of $x$ must be greater than or equal to $3$.
Therefore, the domain of the given function is $[3, +\infty)$.