y=(4x^2+6x+6)/(2x+1) ,x≠-1/2
4x^2+6x+6=y(2x+1)
4x^2+(6-2y)x+6-y=0
要使方程(x为未知数)有解
b^2-4ac>=0
(6-2y)^2-16(6-y)>=0
y^2-2y-15>=0
(y-5)(y+3)>=0
解得值域为:
y<=-3或y>=5