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x-men kurt wagner nightcrawler - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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f(x) = rac{x(x^2 - 3)}{x^2 + 1}
This is smooth and differentiable. Letâs study fixed points: \( f(x)...
rac{x^3 - 3x}{x^2 + 1} = x \Rightarrow x^3 - 3x = x(x^2 + 1) = x^3 + x...
So, only one fixed point at \( x = 0 \).
Now, solve \( f(f(x)) = x \). This includes solutions to \( f(x) = x \...
e x \) â i.e., 2-cycles.
Letâs check the range and behavior. As \( x o \pm\infty \), \( f(x)...
Now, compute \( f(f(x)) - x = 0 \). This is a rational equation; clear...
Let \( y = f(x) \), so \( f(y) = x \). Then:
f(f(x)) = rac{(f(x))^3 - 3f(x)}{(f(x))^2 + 1} = x

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