Proving f inverse is homomorphic

[DPMachine]

I'm trying to show:

If f: S -> S' is an isomorphism of <S, *> with <S', *'>, then f^(-1) is homomorphic.

My take:

So I have to show that f^(-1)(x' *' y') = f^(-1)(x') * f^(-1)(y').

Since f is bijective (onto, more precisely) I know that f^(-1)(x') = x and f^(-1)(y') = y. So f^(-1)(x') * f^(-1)(y') = xy.

How can I simplify f^(-1)(x' *' y') though?

Thanks.

 

[DPMachine]

EDIT: Nevermind, that's not right.

Sorry about not using latex, by the way. I was writing from a mobile device.