# What is surjective function?

## What Does surjective function Mean

In the field of mathematics , a function is called the relationship established between two sets through which each of the elements of the first set is assigned an element –or none– of the second . According to their characteristics, there are different types of functions, such as the 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 image 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 of the first set ( X ) to which it corresponds.
In formal terms, the surjection is written this way : f (x) = y . In this way, each and of Y corresponds to one or more x of X .
The surjective function assumes that the path 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 look at a concrete example to understand what the notion refers to. Let's take the function X → Y defined by f (x) = 4x .
The set X is made up of the elements {2, 4, 6} . The set Y , according to the function, is {8, 16, 24} since
f (2) = 8

f (4) = 16

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

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