How many Possible Functions?

Algebra Level 3

Let f(x)f(x) be a function defined in [0,5][0,5] such that f2(x)=1f^2(x)=1
and x belongs to [0,5][0,5] and f(x)f(x) is discontinuous only at all integers in [0,5][0,5], then the total number of possible functions are

Assume f2(x)=f(x)f(x)f^{2}(x) =f(x) f(x)

I will be happy if anyone will post the solution.
Thanks in advance.

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