Invertible Function

Invertible Function

## Definition / Concept

A function is invertible if there exists a function that reverses its mapping.

## Formula

If:

$$f:A\to B$$

has inverse:

$$f^{-1}:B\to A$$

then:

$$f^{-1}\circ f=I_A$$

$$f\circ f^{-1}=I_B$$

## Conditions / Special Cases

A function has an inverse function if and only if it is bijective.

$$f\text{ is invertible}\Leftrightarrow f\text{ is bijective}$$

## Terminologies

- Inverse function → Function that reverses the mapping of a bijective function.

## Usage

- Used to determine whether a function has an inverse.

- Used in solving equations by reversing a function.