Types of Functions

 

Following are the types of Functions:

(1) One-one function

(2) Many-one function

(3) Onto function

(4) Into function

Let the relation be from set A to set B.

1. One-one function

There is one-one correspondence between the elements of the set A and the set B.

2. Many-one function

There is many-one correspondence between the elements of the set A and the set B.

3. Onto function

Every element of the set B has at least one pre-image.

In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and onto.

4. Into function

There is at least one element of B which has no pre-image.

In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into.

For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions because each function is always one-one onto or one-one into; many-one onto or many-one into.