Question

Define the surjective function. Give an example.

Answer 1

Surjective Function

A function f: A → B is said to be onto if every element in B has at least one pre-image in A. Thus, if f is onto then for each y ∈ B ∃ at least one element x ∈ A such that y = f(x)

Also, f is onto range f = B

Example:

Let N be the set of all natural numbers and let E be the set of all even natural numbers

Let f: N → E: f(x) = 2x Ɐ x ∈ N

Then, y = 2x => x = ½ y

Thus, for each y ∈ E there exists ½ y ∈ N such that

f(1/2 y) = (2 × ½ y) = y

Hence, f is onto.