Final answer:
The domain of the inverse function f⁻¹ is the range of the original function f, which is x.
Step-by-step explanation:
The student asked which of the following is the domain of f⁻¹ (the inverse function), given a one-to-one function f with a domain of x and a range y. The domain of f is the set of all x values for which the function is defined, and the range is the set of all possible outputs or y-values. For a function and its inverse, the domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.
In this case, since the range of f is y, the domain of f⁻¹ would similarly exclude the value that the original range excludes. Thus, the domain of f⁻¹ is x≠(8)/(9).