If I have a mapping under addition $\displaystyle \alpha : \mathbb{z} \rightarrow \mathbb{z}$ given by $\displaystyle \alpha(h(x))=h'(x)$

to show it would I do this-

$\displaystyle \alpha(h(x)+k(x))=\alpha h(x) + \alpha k(x)$

Then when mapping is applied $\displaystyle h'(x)+k'(x)=h'(x)+k'(x)$ and this shows that$\displaystyle \alpha : \mathbb{z} \rightarrow \mathbb{z} \alpha(h(x))=h'(x)$ is a homomorphism? or is there more?