Types of Functions.

According to the nature shown by a Function it can be classified into different types.

They are as following:

1> One-To-One function.

A  Function is said to be a One-To-One Function if every element of Domain of the function have its own and unique element in Range of the Function.

A function from  set A to set B is said to be a One-To-One Function if no two or more elements of set A have same same elements mapped or imaged in set B.

Or no two or more elements processed through the function gives same output.

For example:

When f:A→B is defined by formula y=f(x)=x³ , The function “f” is a One-To-One function because  cube of different numbers is always itself different.

The function “f” in the following Arrow Diagram function is a One-To-One function.

2> Onto Function.

A Function is said to be Onto Function if two or more elements in it’s Domain

have same elements in its Range.

Or , A function from set A to set B is said to be Onto function if two or more elements in set A processed through the function produces same output or same element in set B.

For example:

If set A={a,b,c} and set B={1,2}

And “f” is a function such that f:A→B is defined by:

Then the function “f” is a Onto Function.