Bijective Function

Bijective Function

## Definition / Concept

A function is bijective if it is both one-one and onto.

## Formula

$$f\text{ is bijective}\Leftrightarrow f\text{ is one-one and onto}$$

## Conditions / Special Cases

For finite sets, a bijection between $A$ and $B$ requires:

$$n(A)=n(B)$$

A bijective function has a unique inverse function.

## Usage

- Used to establish one-to-one correspondence between two sets.

- Essential for inverse-function problems.