This statement is True.
When we have two functions, f and g, that are inverses of each other, this means that for every output of function f, there is a corresponding input in function g that will return to the original value.
More specifically, if f: A → B, then g: B → A, where the range of f is the set of outputs found in B, and the domain of g is also the set B (since g takes those outputs and maps them back to inputs in A).
Thus, when f and g are inverses:
- The domain of f (inputs) corresponds to the range of g (outputs).
- The range of f corresponds to the domain of g.
In other words, the domain of f is indeed the same as the range of g. So, the answer to the statement is true.