g(x)= x^2+7

Find the inverse of g(x) and state the domain and range for the inverse of g(x) using interval notation

g(x) has two branches, so

g^-1(x) = ±√(x-7)

in either case, the domain is all x such that x-7 >= 0

just as the range of g(x) is [7,∞)