As the title suggests, I am having difficulty determining what makes one of the functions well-defined and the other not.

I am trying to show/explain why $f([x]\_3)=[5x]\_6$ is not well-defined while $f([x]\_3)=[2x]\_6$ is.

I know that if a function $f: X \longrightarrow Y$ is well defined, then if $x\_1=x\_2 \in X$ then $f(x\_1)=f(x\_2)$.

I started like this...

$f([0]\_3)=[0]\_6$

$f([1]\_3)=[5]\_6$

$f([2]\_3)=[10]\_6=[4]\_6$

I think this last line is where the problem is (why the function is not well-defined) but I'm not sure I am thinking about this the right way. I am just not sure how to use the usual rule. This last line's issue does not come up in the second function.

Any help would be super appreciated. Thanks!