Proving Homomorphism of Groups: Showing f(e)=e' and f(g^-1)=f(g)^-1

[LagrangeEuler]

Homework Statement

Show that
$f(e)=e'$ and $f(g^-1)=f(g)^-1$

Homework Equations

Homomorphism
f(x\cdot y)=f(x)\cdot f(y)

The Attempt at a Solution

I show the first one. Neutral element is element which satisfied
$e\cdot e=e$.
So
$f(e)=f(e\cdot e=e)=f(e)\cdot f(e)$
So $f(e)=e'$.
But how to show
$f(g^{-1})=f(g)^{-1}$?

 

[pasmith]

Homework Statement

Show that
$f(e)=e'$ and $f(g^-1)=f(g)^-1$

Homework Equations

Homomorphism
f(x\cdot y)=f(x)\cdot f(y)

The Attempt at a Solution

I show the first one. Neutral element is element which satisfied
$e\cdot e=e$.
So
$f(e)=f(e\cdot e=e)=f(e)\cdot f(e)$
So $f(e)=e'$.

But how to show
$f(g^{-1})=f(g)^{-1}$?

What is f(gg^{-1})?

 

[LagrangeEuler]

Tnx.