Let $f$ be an injection, then the converse $f^{-1}$ is also a function and is called the inverse of $f$.
For any injection $f$:
- \[f\circ f^{-1} = \id_{\ran f}.\]
- \[f^{-1}\circ f = \id_{\dom f}.\]
Let $f$ be an injection, then the converse $f^{-1}$ is also a function and is called the inverse of $f$.
For any injection $f$:
- \[f\circ f^{-1} = \id_{\ran f}.\]
- \[f^{-1}\circ f = \id_{\dom f}.\]