The point is that "inverse" usually refers to the function that reverses the effect of the original function, i.e. f_inv(f(x)) = x for all x in Domain(f) g(

The point is that "inverse" usually refers to the function that reverses the effect of the original function, i.e. f_inv(f(x)) = x for all x in Domain(f) g(x) = 1 / sqrt(x) is not the inverse of f(x) = sqrt(x) in this sense.