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

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