# 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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