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Home » You Won’t Believe What Happened When This m Bison Broke INTO My Life! - Coaching Toolbox

You Won’t Believe What Happened When This m Bison Broke INTO My Life! - Coaching Toolbox

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 rac{x^3 - 3x}{x^2 + 1} = x \Rightarrow x^3 - 3x = x(x^2 + 1) = x^3 + x \Rightarrow -4x = 0 \Rightarrow x = 0

📌 So, only one fixed point at \( x = 0 \).

📌 Now, solve \( f(f(x)) = x \). This includes solutions to \( f(x) = x \) (fixed points) and solutions where \( f(f(x)) = x \) but \( f(x)

📌 e x \) â i.e., 2-cycles.

📌 Letâs check the range and behavior. As \( x o \pm\infty \), \( f(x) \sim x^3 / x^2 = x o \mp\infty \), so \( f(x) \) is odd asymptotically.

📌 Now, compute \( f(f(x)) - x = 0 \). This is a rational equation; clear denominators:

📌 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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