Let me see. To be exact, the domain of the first term is all such that
, which implies
So that's all the points inside or on the boundary of the circle of radius 2 centered at the origin.
The domain of the second term is all such that
which implies or
There are three regions involved here: You also have the boundary points which are clearly in the domain, since equality is allowed. If you plug in numbers, you can see that it is only the values in that are allowed. doesn't matter in this second piece.
So, finally, to answer your question: you must take the intersection of these two regions, because if you go outside either of them, one part of your function will not be defined (if you're assuming you have real functions, which I am assuming).
Does this make sense?