JEE Math Practice Question

Let N be the set of natural numbers and two functions f and g be defined as f, g : N $$ \to $$ N such that f(n) = $$\left\{ {\begin{matrix} {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \\ {{n \over 2};} & {if\,\,n\,\,is\,\,even} \\ \end{matrix} \,\,} \right.$$; and g(n) = n $$-$$($$-$$ 1)n. Then fog is -

1. A.neither one-one nor onto
2. B.onto but not one-one
3. C.both one-one and onto
4. D.one-one but not onto