Let $\displaystyle G_1$ and $\displaystyle G_2$ be groups with identities $\displaystyle e_1$ and $\displaystyle e_2$, respectively. Let $\displaystyle f: G_1 \to G_2$ be a homomorphism of groups. Let $\displaystyle K$ be the kernel of $\displaystyle f$. Let $\displaystyle x \in K$. Which of the following is/are necessarily true?

a) $\displaystyle x = e_1$

b) $\displaystyle x = e_2$

c) $\displaystyle f(x) = e_2$

d) $\displaystyle f(x) = e_1$

e) $\displaystyle f(x) = e_1e_2$

I've never taken abstract algebra before so I have never seen anything like this. Any help would be greatly appreciated.