Question

Given sets A and B, what is the function f: A->B?

Answer 1

f: A→B be a function.

If each element in the codomain ‘ B‘ has at least one pre-image in the domain A that is, for every b ∈B there exists at least one element a ∈ A such that f(a) = b, then f is onto.

In other words range of f = B , for onto functions.

On the other hand if there exists at least one element in the codomain B which is not an image of any element in the domain A, then f is into.

Onto function is also called Surjective function and a function which is both one-one and onto is called Bijective function.

e.g. f : R->R where f(x) = sinx is into.

f : R−>R where f(x) = ax³ + b is onto where a ≠ 0 , b∈ R.