f(x+y)-f(y)=(x+2y+1)x
设x＞0,y＞0,有x+y＞y,(x+2y+1)x＞0
即f(x+y)-f(y)=(x+2y+1)x＞0
则f(x)在(0,+∞)上递增
f(1+0)-f(0)=f(1)-f(0)=(1+1)·1
-f(0)=2
f(0)=-2
f(1/2+1/2)-f(1/2)=f(1)-f(1/2)=(1/2+2·1/2+1)/2
-f(1/2)=5/4
f(1/2)=-5/4
f(x)+3＜2x+a,x∈(0,1/2),f(x)∈(-2,-5/4)
f(x)＜2x+a-3,x∈(0,1/2),f(x)∈(-2,-5/4)
2·1/2+a-3≥-5/4
a≥3/4
a的取值范围a≥3/4