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Problem of the Week 891

A Funny Function

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Suppose f is a continuous function such that f(1000)=999 and f(x) · f(f(x)) = 1 for all real x. What is f(891)?

Source: A Polish Mathematical Olympiad, as reported in Crux Mathematicorum, May 1999 p. 229

© Copyright 1999 Stan Wagon. Reproduced with permission.

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