Let \( R \) be the set of real numbers and \( f: R \rightarrow R \)...

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Let \( R \) be the set of real numbers and \( f: R \rightarrow R \) be such that for all \( x \& y \) in \( R \) \( |f(x)-f(y)| \leq|x-y|^{3} \). Prove that \( f(x) \) is constant.
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