Small problem with Groups

Hi

I am struggling with the following questions:

Let H be a subgroup of the group G.

i) Show that H is a right coset and that the distinct right cosets og H are disjoint

ii) Show that the map f: G/H -> H/G given by f(gH)=Hg^-1 is well defined and bijective.

For i) I have shown the last part where i take two cosets of H; Ha and Hb which are not disjoint and show that Ha=Hb.

So I really need some help for the first part of i) and for ii)

Best regards