函数f(x)=sinx-根号3cosx(x∈【-π,0】)的值域为

f(x)=sinx-根号3cosx
=2[sinx*(1/2)-cosx*(√3/2)]
=2[sinx*cos(π/3)-cosx*sin(π/3)]
=2sin(x-π/3)
x∈【-π,0】
x-π/3∈【-4π/3,-π/3】
sin(x-π/3)∈【-1,√3/2】
所以 y∈【-2,√3】