In the field of math, is called function to relationship that is established between two sets through which, each of the elements of the first set, he is assigns one element – or none – of the second. Depending on their characteristics, there are different types of functions, such as injective function, the logarithmic function, the exponential function and the quadratic function, among many others.

The surjective function implies that each element of the second set is the picture of at least one element of the first set. This function is also known as subjective, surjective, surjective, epjective or exhaustive.

It can be said that, in a surjective function, each element of the second set (which we can call Y) has at least one element from the first set (X) to which it corresponds.

In formal terms, the surjective function is written like this mode: f (x) = y. In this way, each Y of Y corresponds to one or more x of X.

The surjective function assumes that the route of the function is the second set (Y). That is why it can be stated that in a surjective function the path and the domain (starting set or definition set) are equal.

Let’s see a example concrete to understand what the notion alludes to. Let’s take the function X → Y defined by f (x) = 4x.

Set X is made up of the elements {2, 4, 6}. Set Y, according to the function, is {8, 16, 24} as

f (2) = 8
f (4) = 16
f (6) = 24

Therefore, f: {2, 4, 6} → {8, 16, 24} defined by f (x) = 4x turns out a surjective function.