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)?

If f(x) = 1/x, then the inverse relationship applies across the entire domain.

But we are told that f(f(x)) = 1/f(x).

Let y = f(x). Then the domain of y is the range of x.

Then f(y) = 1/y, if y is in the range of f(x)