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f(x)=x3−3xf(x)=x^3-3xf(x)=x3−3x
Find the closed form of fn(x),f^n(x),fn(x), and then find the number of distinct real solutions of f16(x)=2.f^{16}(x)=2.f16(x)=2.
Note: fn(x)f^n(x)fn(x) is the nthn^\text{th}nth composition of f,f,f, that is, fn(x)=f∘f∘⋯∘f⏟n times(x). f^n(x) = \underbrace{f \circ f \circ \cdots \circ f}_{n \text{ times}}(x).fn(x)=n timesf∘f∘⋯∘f(x).
Bonus: If g(x)=2+x,g(x)=\sqrt{2+x},g(x)=2+x, find the closed form of gn(x).g^n(x).gn(x).
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