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Define the function f(x)=2x1−x2f(x)=\frac{2x}{1-x^2}f(x)=1−x22x. Find the number of distinct real solutions of the equation f(5)(x)=x.f^{(5)} (x) =x.f(5)(x)=x.
Details and assumptions
f(n)(x) f^{(n)} (x) f(n)(x) denotes the function fff applied nnn times. In particular, f(5)(x)=f(f(f(f(f(x))))) f^{(5)} (x) = f(f(f(f(f(x)))))f(5)(x)=f(f(f(f(f(x))))).
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