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?
by
Prince Loomba