In mathematics, a surjective function (also known as surjection, or onto function) is a function f that maps an element x to every element y; that is, for every y, there is an x such that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain.

How do you know if a function is onto?

Mathematically, if the rule of assignment is in the form of a computation, then we need to solve the equation y=f(x) for x. If we can always express x in terms of y, and if the resulting x-value is in the domain, the function is onto.

What is an example of a onto function?

Examples on onto function

Example 1: Let A = {1, 2, 3}, B = {4, 5} and let f = {(1, 4), (2, 5), (3, 5)}. Show that f is an surjective function from A into B. The element from A, 2 and 3 has same range 5. So f : A -> B is an onto function.