#### Answer

$[3, \infty)$

#### Work Step by Step

Let $f(x)=({x-3})^{1/2}(x+4)^{-1/2}$
In order to find the domain we will have to set the equation inside the square root greater than and equal to zero.
we have, ${x-3} \geq 0$ and $x+4 \gt 0$
or, $x \geq 3$ and $x \geq -4$
Thus, Domain for $f(x)=({x-3})^{1/2}(x+4)^{-1/2} $ will be a set of interval to both domains, that is, $[3, \infty)$