Bloody Roots

Algebra Level 3

Consider a function \(f(x)\) such that \(f(2)=f(6)=0\). Evaluate the sum of all right sentences.

(1) \(f(x) = k(x^2 - 8x + 12), k \in \mathbb{Z}\)

(2) \(f(1) \cdot f(7) \geq 0\)

(4) \(f(f(2)) = f(f(6))\)

(8) \(f(4) \in \mathbb{C}\)

(16) If \(\displaystyle k^{ \displaystyle k^{ ( \cdots) }} = 2\), then \(f(4 \pm k^2) = 0 \).

(32) \(f^{(2014)}(x) = k, k \in \mathbb{R}\)

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