已知函数f(x)=(cx+d)/(ax+b),其中a≠0,ad-bc≠0,试讨论f(x)的单调性

问题描述:

已知函数f(x)=(cx+d)/(ax+b),其中a≠0,ad-bc≠0,试讨论f(x)的单调性

f(x)=(cx+d)/(ax+b)=c/a(ax+b-b+ad/c)/(ax+b)=c/a+(ad-bc)/c(ax+b)=c/a+(ad/c-b)/(ax+b)=c/a+(d/c-b/a)/(x+b/a)(1) d/c-b/a>0 f(x)在(-无穷,-b/a)(-b/a,+无穷)上是减函数(2) d/c-b/a