Find the limit of composition 2

Calculus Level 3

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

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

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

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

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