I'm given a function f and the unit disk (although it could be any region)
Does the above mean the domain of the function is the unit disk or the codomain?
is the codomain if is the domain. Then would be the correct notation. Using the symbol implies that f is a member of a collection of functions not points. In short, I wouldn't call a valid statement (unless in this case, D is a collection of functions, which I've never seen written this way).