Functional equation.

 Dear Phorum Participants!
Please help to find all functions f(x,y), which satisfy the following
two conditions:
1. f(x,1/x)=x, for all x > 0,
2. f(x,y)*f(y,x)=1, for all x > 0, y > 0.

Here x > 0, y > 0 are independent variables, and function f(x,y) is
supposed to be "well-behavied" enough you require.

Thank you very much for any assistance, Mikhail.