设x1>x2>-2
f(x1)-f(x2)=[(ax1+1)(x2+2)-(ax2+1)(x1+2)]/[(x1+2)(x2+2)]
=[(2a-1)(x1-x2)]/[(x1+2)(x2+2)]
当a>1/2时,f(x1)-f(x2)>0
∴当a>1/2时,f(x)在区间x∈(-2,正无穷）上单调递增