Almost. What you give is a subset of therangeof f and I believe you want the domain. The domain of is thesubset of the domain of fthat is mapped into that intersection. And since that is necessarily a subset of the range of f, you don't need to say that. Oh, and you have the order of the functions reversed. The domain of is . The domain of is .

The answer to the question given, is "No, the is not necessarily contained in the domain of f, it is contained in the domain ofg". A counterexample to the original statement is g(x)= -x, f(x)= . so its domain is the set of all non-[b]positive[/tex] numbers while the domain of f is the set of all non-negative numbers.