Quoting " Let $\phi : Z \rightarrow Z$ be given by $\phi(n) = 7n$. Prove that $\phi$ is a group homomorphism. Find the kernel and the image of $\phi$."
Whether proving that we have a homomorphism or proving we have a group homomorphism, isn't it the same proof process?
I prove that it is a group homomorphism by showing that: $$\phi(x \circ y) =\phi(x) . \phi(y) $$ ($x,y \in Z$ and group operation $\circ$ and $.$ are both addition).
Any input is much appreciated.