已知f(x)=x/x-a(x≠a).(1)若a=-2,试证f(x)在(-∞,-2)内单调递增;(2)若a>0且f(x)在(1,+∞)内单调递减,求a的取值范围.

问题描述:

已知f(x)=

x
x-a
(x≠a).
(1)若a=-2,试证f(x)在(-∞,-2)内单调递增;
(2)若a>0且f(x)在(1,+∞)内单调递减,求a的取值范围.

(1)证明任设x1<x2<-2,则f(x1)-f(x2)=x1x1+2-x2x2+2 =2(x1-x2)(x1+2)(x2+2).∵(x1+2)(x2+2)>0,x1-x2<0,∴f(x1)-f(x2)<0即f(x1)<f(x2),∴f(x)在(-∞,-2)内单调递增.(2)解任...