Surjective Functions

A Function is surjective when all elements of the co-domain are mapped to.

This is also called "Onto"

Formally:

yY,xX s.t. f(x)=y\forall y\in \mathbb{Y}, \exists x \in \mathbb{X} \text{ s.t. } f(x)=y

or "For all elements yy in Y\mathbb{Y}, there exists an xx in X\mathbb{X} such that ff at xx is equal to yy

Surjective Function Example

Exercise

Show that if two functions ff and gg are Surjective so is gfg \bullet f. Show an example of where gfg \bullet f is Surjective but ff is not.