Suppose

fis a continuous function such thatf(1000)=999 andf(x) ·f(f(x)) = 1 for all realx. What isf(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