Abstract Algebra: Proving a property related to group isomorphism 
Possible Duplicate:
Proof of first isomorphism theorem of group 

Let $G_1, G_2$ be groups. If $f: G_1 \rightarrow G_2$ is a group homomorphism with $K = \ker(f)$, then $G_1 / K$ is isomorphic to $f(G_1)$.
This was a theorem in the book that was left unproven and I'm really curious as to how you would go about it. 

You can get this theorem from any starting Algebra book, you can refer Herstein. But why not try yourself?
First prove that $\ker (f)$ is subgroup in $G_1$ (in fact it's a normal subgroup). Then
Define $h: G_1/\ker(f) = G_2$ by $h(g_1 + (\ker f)) = f(g_1)$, and check if this is isomorphism or not.
