Properties of function $\mathbb{Z_6} \to \mathbb{Z_6}$ : $x \to 4x$ where arithmetic is done modulo 6

Question

$f : \mathbb{Z_6} \to \mathbb{Z_6}$ : $x ↦ 4 x$ where arithmetic is done modulo 6.

I know that $\Bbb Z$ means integers and $x ↦ 4 x$ is the same as $f(x) = 4x$, but other than that im not sure how to proceed, especially when it comes to modulo $6$.

The question then asks if $f$ is a $1-1$ function, or is $f$ an onto function?

My lecturer isnt very good, any help is appreciated.

Answer 1

It is not 1-1 beause f(0) = f(3).