Please can you help me with this question:

Define the following map on a cyclic finite group G:

f:G--> G x|-->f(x):=x^m

where m is a fixed interger prove f is a group morphism and establish one condition whether sufficent of necessary for f to be a monomorphism.

I know that x^m is a cyclic group

I also know a monomorphism is an injective homomorphism, which is one to one as a function which relates maybe to f:G-->G.

When it asks to prove it is a group morphism does this mean I need to find the kernal and the image.

I know what the question means but just don't know the proof of it.

Any help would be great thanks