More fun in 2015, part 16?

Calculus Level 5

Define a function \(f : \mathbb R \to \mathbb R\) such that it satifies

\(f(f(x)) = f(x)^{2015}\)

Then how many polynomial functions satifies the above equation?

Bonus :- how many functions satifies the above relation? (don't input this as an answer)

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