Question 12
(GBR 4) IMO1. Find all functions $f$ defined on the positive real numbers and taking positive real values that satisfy the following conditions:
(i) $f(xf(y))=yf(x)$ for all positive real $x,y$.
(ii) $f(x)\to0$ as $x\to+\infty$.
(i) $f(xf(y))=yf(x)$ for all positive real $x,y$.
(ii) $f(x)\to0$ as $x\to+\infty$.