The statement is true. When two functions, f and g, are inverse functions, they essentially reverse the effect of each other. This means that the output of function f will feed into function g to produce the original input.
To elaborate, let’s define some terms:
- Domain of f: This is the set of all possible input values (x) for the function f.
- Range of g: This is the set of all possible output values (y) that can be obtained from the function g.
Now, if we look at the relationship between these two functions, if f(x) = y implies that g(y) = x, then it follows that for every input x in the domain of f, the corresponding output y will lie in the range of g.
Conversely, for every output y in the range of g, there exists an input x in the domain of f that produces it. Therefore, the domain of f is indeed the same as the range of g.
In summary, knowing that f and g are inverse functions directly leads us to the conclusion that the domain of f matches the range of g, solidifying our understanding of their interconnectedness in functional relationships.