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Consider the function f(x)=x3 f(x) = x^3 f(x)=x3. Let f(n)(x)=f(f(n−1)(x)) f^{(n) } (x) = f\left( f^{(n-1)} (x) \right) f(n)(x)=f(f(n−1)(x)) be the function composed nnn times.
Define the function F:R→ F: \mathbb{R} \rightarrow F:R→ extended reals (including infinity) by
F(x)=limn→∞f(n)(x). F(x) = \lim_{n\rightarrow \infty} f^{(n)} (x). F(x)=n→∞limf(n)(x).
How many points of discontinuity does F(x) F(x) F(x) have?
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