Inverse Function

🅟 Feb 22, 2026

  🅤 Mar 02, 2026

DEF-FI. Inverse Function.

Let $f$ be a function. If $f$ is injective, then the converse $f^{-1}$ is also a function and is called the inverse of $f$.


PROP-FI-ID.

For any injection $f$:

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