\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : [0, 1] \to \mathbb{R}\) continuous with \(f(0) = f(1)\). Show that there exists \(c \in [0, 1/2]\) such that \(f(c) = f(c + 1/2)\).
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