已知向量a=(sinx,3/2),向量b=(cosx,-1).求f(x)=(向量a+向量b)*向量b在[-π/2,0]上的值域

由f(x)=(向量a+向量b)*向量b
=(sinx+cosx,3/2-1)*(cosx,-1)
=sinxcosx+(cosx)^2-1/2
=(1/2)sin2x+(1/2)cos2x+1/2-1/2
=(√2/2)sin(2x+π/4)
当x∈[-π/2,0]时2x+π/4∈[-3π/4,π/4]
即sin(2x+π/4)∈[-1,√2/2]
即值域为[-√2/2,1/2]