用定义证明f(x)=（ax+1）/(x+2),(a不等于0.5)在（负无穷,-2）上的单调性

Question

用定义证明f(x)=（ax+1）/(x+2),(a不等于0.5)在（负无穷,-2）上的单调性

Answer 1

设任意x1,x2∈(-∞,-2),其中x2>x1.
f(x2)-f(x1)=(ax2+1)/(x2+2)-(ax1+1)/(x1+2)
=[(ax2+1)(x1+2)-(ax1+1)(x2+2)]/(x1+2)(x2+2)
=(x2-x1)(2a-1)/(x1+2)(x2+2)
当a>0.5时,总有f(x2)-f(x1)>0,即增函数
当a