Let G1 and G2 be groups and let f:G1 -> G2, be an isomorphism. If G1 is a cyclic group with generator a, prove G2 is also a cyclic group with generator f(a).

Ok so i did this, teacher said it was wrong and that i need to show G1 and G2 have the same order. And that G1=<a> so i need to prove G2=(f(a))

So where do i start and how do i end?