f(x)=2x-a/x(a为实数)的定义域为(0,1】（a为实数）
令0＜x1＜x2≤1
f(x2)-f(x1) = 【2x2-a/x2】-【2x1-a/x1】
= 2(x2-x1) + a(1/x1-1/x2)
= 2(x2-x1) + a(x2-x1)/(x1x2)
= (x2-x1)(2x1x2+a)/(x1x2)
∵x1＜x2,∴x2-x1＞0
∵0＜x1＜x2,∴x1x2＞0
∵0＜x1＜x2≤1,∴0＜x1x2＜1
当a≥0时,2x1x2+a＞0恒成立,此时f(x2)-f(x1)= (x2-x1)(2x1x2+a)/(x1x2)＞0,f(x)在(0,1】单调增；
当a≤-2时,2x1x2+a＜0恒成立,此时f(x2)-f(x1)= (x2-x1)(2x1x2+a)/(x1x2)＜0,f(x)在(0,1】单调减；
当-2＜a＜0时,f(x)在(0,1】非单调.