# Nature of Functions

__One – One Function:__

Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘’ from A to B is called a one–one function, if and only if distinct elements of set A have distinct elements of set B.

e.g. ,

Mathematically,

Let be a function then ‘’ is called a one–one function if and only if

(i)

(ii)

** Onto Function**:

Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘’ from A to B is called an onto function if and only if the range of

e.g. ,

__Bijective Function:__

A function which is one–one as well as an onto function is called a bijective function.

e.g.,