Editing Monotonic function (section)

=== Inverse of function ===

All strictly monotonic functions are [[Inverse function|invertible]] because they are guaranteed to have a one-to-one mapping from their range to their domain.

However, functions that are only weakly monotone are not invertible because they are constant on some interval (and therefore are not one-to-one).

A function may be strictly monotonic over a limited a range of values and thus have an inverse on that range even though it is not strictly monotonic everywhere. For example, if <math>y = g(x)</math> is strictly increasing on the range <math>[a, b]</math>, then it has an inverse <math>x = h(y)</math> on the range <math>[g(a), g(b)]</math>.

The term ''monotonic'' is sometimes used in place of ''strictly monotonic'', so a source may state that all monotonic functions are invertible when they really mean that all strictly monotonic functions are invertible.{{cn|reason=Give an example for such a source.|date=August 2022}}