Inverse Function

🅟 Feb 22, 2026

  🅤 Jun 10, 2026

Definition 1.

For any injection $f$, its converse $f^{-1}$ is also a function, called its inverse.


Proposition 1.

For any injection $f$:

  1. \[f \circ f^{-1} = \id_{\im f}.\]
  2. \[f^{-1} \circ f = \id_{\dom f}.\]