If $\space o(\ker\phi) = n$, then $\varphi$ is an $n$-to-$1$ mapping from $G$ onto $\varphi(G)$ If $G,H$ are groups and $\varphi\colon G\to H$ a group homomorphism, how can I prove that if the order of $\ker\phi$ is $n$ then $\varphi$ is an $n$-to-$1$ mapping from G onto $\varphi(G)$

Hint: Given $g\in G$, which $x\in G$ satisfy $\phi(xg)=\phi(g)$?
