Sets, Relations and Functions: JEE Main 2019 Mathematics 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) = $\left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.$;       and g(n) = n $-$($-$ 1)^n. Then fog is -