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?