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Constant function


Let g: \mathbb{R} \to \mathbb{R} be a continuous function such that \lim_{x\to \infty}g(x)-x=\infty and such that the set \{x : g(x)=x\} is finite and nonempty. Prove that if f: \mathbb{R} \to \mathbb{R} is continuous and f\circ g=f, then f is constant.
AMM 10818

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