Mark M. answered 04/05/21
Retired college math professor. Extensive tutoring experience.
For g(x) = √(x-7), the domain is [7, ∞) and the range is [0, ∞).
For g-1(x), the domain is the same as the range of g(x) and the range of g-1(x) is the same as the domain of g(x).