Find the limit of composition 2

Calculus Level 3

Consider the function f(x)=x3 f(x) = x^3 . Let f(n)(x)=f(f(n1)(x)) f^{(n) } (x) = f\left( f^{(n-1)} (x) \right) be the function composed nn times.

Define the function F:R F: \mathbb{R} \rightarrow extended reals (including infinity) by

F(x)=limnf(n)(x). F(x) = \lim_{n\rightarrow \infty} f^{(n)} (x).

How many points of discontinuity does F(x) F(x) have?

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