# How many Possible Functions?

Let $f(x)$ be a function defined in $[0,5]$ such that $f^2(x)=1$
and x belongs to $[0,5]$ and $f(x)$ is discontinuous only at all integers in $[0,5]$, then the total number of possible functions are

Assume $f^{2}(x) =f(x) f(x)$

I will be happy if anyone will post the solution.