 A function that is monotonic, but not strictly monotonic, and thus constant on an interval, doesn't have an inverse.This is because in order for a function to have an inverse there needs to be a one-to-one mapping from the range to the domain of the function, since a monotonic function has some values that are constant in its domain, this means that there would be more than one value in the range that maps to this constant value.However, a function y=g(x) that is strictly monotonic, has an inverse function such that x=h(x) because there is guaranteed to always be a one-to-one mapping from range to domain of the function.