Let A ={1,2,3, …, 10} and f: A → A be defined as f(k)= {k+1, if k is odd; k, if k is even} Then the number of possible functions g: A → A such that g…

Let $\displaystyle \mathrm{A}=\{1,2,3, \ldots, 10\}$ and $\displaystyle f: \mathrm{A} \rightarrow \mathrm{A}$ be defined as $$f(k)=\left\{\begin{array}{cl} k+1 & \text { if } k \text { is odd } \\ k & \text { if } k \text { is even } \end{array}\right. $$ Then the number of possible functions $\displaystyle g: \mathrm{A} \rightarrow \mathrm{A}$ such that $\displaystyle g o f=f$ is :