Final answer:
The domain of the inverse function g^-1(x) will be x > 0, and its range should be y < 2, assuming a typical direct swap of domain and range without additional constraints, even though this isn't represented in the provided options.
Step-by-step explanation:
The domain and range of a function and its inverse are closely related. For a function g(x) with a domain of x < 2 and a range of y > 0, its inverse function, g-1(x), will have the domain and range switched. Therefore, the domain of g-1(x) will be the range of g(x), which is x > 0, and the range of g-1(x) will be the domain of g(x), which means y < 2. However, because y is the output of g-1(x), it must also satisfy the condition given originally for g(x)'s range, which is y > 0. Combining these two conditions for y in the inverse function, y must be greater than 0 but also less than 2, which isn't an option provided. Thus, it seems there's an error in the provided options or question. However, assuming the intended question represents typical scenarios where the inverse function's domain and range strictly swap without additional constraints, the corresponding answer would typically be Domain: x > 0 and Range: y < 2.