Hi, I've got this question which I'm sure should be easy but I just don't seem to be able to get started...

I have a centre of a group G defined as

Z(G) = {x is an element of G : for all y contained in G xy=yx}.

Also k: G is mapped to G is an automorphism of G and automorphisms form a group Aut(G) under composition.

I have to show that the function f: G is mapped to Aut(G) defined by

[f(g)](h) = ghg^-1 is a group homomorphism.

I know that I have to show that f(g1,g2) = f(g1)f(g2) but I don't know how to go about it when the function is defined the way it is.

Any hints or advice would be very much apprecaited.

THANKS!