Consider the function F(x,y) = √x+ y . What is the domain of F?
Domain is what values you are "allowed" to put in for x (is a good way to think of it). I am presuming the problem is really this: F(x,y) = √ (x + y) ; where both x and y are under the radical.
Assuming that is what the problem is, and you do not want a negative under an even radical; you would want (x+y) ≥ 0. Taking this, you would do a bit of algebra to get y on one side, and y ≥ -x, the third option above.
Does the process make sense to you? I trust!