Closing \(f^n\)

Geometry Level 3

\[f(x)=x^3-3x\]

Find the closed form of \(f^n(x),\) and then find the number of distinct real solutions of \(f^{16}(x)=2.\)

Note: \(f^n(x)\) is the \(n^\text{th}\) composition of \(f,\) that is, \( f^n(x) = \underbrace{f \circ f \circ \cdots \circ f}_{n \text{ times}}(x).\)


Bonus: If \(g(x)=\sqrt{2+x},\) find the closed form of \(g^n(x).\)

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