How to find know if function is onto? How do you figue out whether this function is onto?
$\mathbb{Z}_3\rightarrow \mathbb{Z}_6:f(x)=2x$
Onto is of course is for all the element b in the codomain there exist an element a in the domain such that $f(a)=b$
Here the co domain is mod 6
So let $k\in\mathbb{Z}_6$
But I am not sure how to see if it is onto.

To put it a bit differently from Bananarama, the map gives you the values {$f(0),f(1),f(2)$}$(Mod 6)$. Even if these values are a different, can the map be onto?
