证明：任取x1，x2∈（0，1]，且x1＜x2，则f(x1)−f(x2)＝(x1+1x1)−(x2+1x2)＝(x1−x2)(x1x2−1)x1x2，∵0＜x1＜x2≤1，∴x1-x2＜0，x1x2-1＜0，x1x2＞0，∴f（x1）-f（x2）＞0，即f（x1）＞f（x2），∴f(x)＝x+1x在...