Definition:Inverse Mapping/Also known as

Inverse Mapping: Also known as
If $f$ has an inverse mapping, then $f$ is an invertible mapping.

Hence, when the inverse (relation) of $f^{-1}$ is a mapping, we say that $f$ has an inverse mapping.

Some sources, in distinguishing this from a left inverse and a right inverse, refer to this as the two-sided inverse.

Some sources use the term converse mapping for inverse mapping.