函數 y = (ax+2)/(x+2) 在( -2,+∞)上是單調增函數,求實數a的范圍

熱心網友

解:y=(ax+2)/(x+2) =(ax+2a+2-2a)/(x+2) =a+(2-2a)/(x+2) 當x-2時,x+20,所以1/(x+2)是減函數 因為整個函數為增函數,y=(ax+2)/x+2 =[a(x+2)-2a+2]/x+2 =a-(2a-2)/x+2 (-2,+∞ )上為增函數,所以2a-20 ==a1