# Injective, Surjective and Bijective Functions

Let us consider a function from A to B and understand the types of function:**General Function**– We have already discussed this. Two or more elements of A can have same mapping in B.*y*=*f*(*x*) =*x*^{2}. In this function, two values of*x*will point to same value of*y*. (*x*= 2 or*x*= –2 both will give*y*= 4).**Injective**– In this type of functions, each element in A has its unique corresponding mapping in B. B may have some elements without any correspondence in A.*y*=*f*(*x*) = 3*x*+ 2

In this case, you won’t have two values of A having same mapping in B. So “many to one” is not possible. (One to many is obviously not possible because it’s a function).**Surjective**– In this type of functions, each element in B should be mapped by one or more than one element in A.**Bijective**– It means both Injective and Surjective.

Example-1

Indentify what type of function is this (

*x*to*y*)?-
(i) A general function

(ii) Injective

(iii) Surjective

(iv) Bijective -
(i) A general function

(ii) Injective

(iii) Surjective

(iv) Bijective -
(i) A general function

(ii) Injective

(iii) Surjective

(iv) Bijective

Solution

- Bijective is the answer.
- A general function is the answer because many to one mapping is there.
- It cannot be Injective because two X are pointing to single Y. Since no Y is left out, hence Surjective is the answer.