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)?

f(f(x)) = 1 / f(x)
If x=1000, then f(999) = 1 / 999
In fact it seems like f(x) should be 1 / x;
but f(1000) is not 1/1000, it is 999.

So at first glance it does not seem such a function can be continuous.

I must be missing something.
How about: Neither f(x) nor f(f(x)) can ever be zero.

That doesn't help either

Posted by Larry on 2013-08-02 08:28:56