=loga((x+2-4)/(x+2))
=loga(1-4/(x+2))
1-4/(x+2)是增函數(shù)
又f(x)在[α,β]上是減函數(shù)
所以0
f(x)在[α,β]上是減函數(shù)
所以f(β)=log(a)a(β-1)
log(a)(1-4/(β+2))=log(a)a(β-1)
1-4/(β+2)=a(β-1)
β-2=a(β-1)(β+2)
同理可知
α-2=a(α-1)(α+2)
即方程
x-2=a(x-1)(x+2)有兩解-2
ax^2+(a-1)x=0
ax(x+(a-1))=0
x1=0 x2=1-a
所以 -2<1-a<2
-1