Let $A = \{ 1,2,3,....,10\} $ and $f:A \to A$ be defined as$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$Then the number of possible functions $g:A \to A$ such that $gof = f$$ is :

Question

Let $A = \{ 1,2,3,....,10\} $ and $f:A \to A$ be defined as

$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$

Then the number of possible functions $g:A \to A$ such that $gof = f$$ is :