Problem of the Week 891

A Funny Function

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.

15 September 1999