Let R⁺ denote the set of positive real numbers. Find all functions f:R⟶R such that for each x∈R⁺, there is exactly one y∈R⁺ satisfying：

xf(y)+yf(x)≤2.

译文：

设R⁺表示所有正实数构成的集合.求所有函数f:R⁺→R⁺，使得对任意x∈R⁺，恰好有一个y∈R⁺满足条件：xf(y)+yf(x)≤2.