jmc

Question

The function f(x,y) satisfies f(x,y) = x + yf(y,x)for all real numbers x and y such that xy 1. Find f(1,2).

Accepted Answer

Setting x = 1 and y = 2, we get f(1,2) = 1 + 2f(2,1).Setting x = 2 and y = 1, we get f(2,1) = 2 + f(1,2).Then f(1,2) = 1 + 2(2 + f(1,2)) = 5 + 2f(1,2), so f(1,2) = -5.