APSC 174: Linear Algebra for Engineers

A Function is injective when different elements of the domain are mapped to different elements of the codomain.

This is also called "One-to-One"

Formally:

\forall x_1, x_2 \in \mathbb{X}, f(x_1)=f(x_2) \Rightarrow x_1=x_2

or "For all elements $x_1, x_2$ in $\mathbb{X}$ . If $f$ of $x_1$ equals $f$ of $x_2$ that implies that $x_1$ equals $x_2$ "

Injective Function Example

Exercise

Show that if $g \bullet f$ is Injective then $f$ is Injective. Show an example of where $g \bullet f$ is Injective but $g$ is not.