f(x)=2√3sinxcosx-2cos(x+π/4)cos(x-π/4)
=√3sin2x+2sin(x+π/4-π/2)cos(x-π/4)
=√3sin2x+sin(2x-π/2)
=√3sin2x-cos2x
=2sin(2x-π/6)
T=2π/2=π
2x-π/6=π/2+kπ,k是整数
对称轴x=π/3+k/2π,k是整数
x∈【-π/12,π/2】
2x-π/6∈[-π/3,5/6π]
f(x)属于【-√3,2】
望采纳