A constant continuous function – math.stackexchange.com

A constant continuous function – math.stackexchange.com

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Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous function such that $f(x)=f(x^2)$ for all $x\in\mathbb{R}$. I've proven that also $f(y^{(2^{-n})})=f(y)$ for all $n\in\mathbb{N}, y\geq0$. How can I ...

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