f(x)=√3sin2x+2sin(x-π/4)sin(x+π/4)
=√3sin2x+2(sinxcosπ/4-cosxsinπ/4)(sinxcosπ/4+cosxsinπ/4)
=√3sin2x-cos2x
=2sin(2x-π/6)
当x∈[-π/12,π/2],(2x-π/6)∈[-π/3,5π/6],则f(x)∈[-√3,2]
于是-√3-m≤f(x)-m≤2-m
所以-√3-m>-2且2-m f(x)=√3sin2x+2sin(x-π/4)sin(x+π/4)
=√3sin2x+2(sinxcosπ/4-cosxsinπ/4)(sinxcosπ/4+cosxsinπ/4)
=√3sin2x-cos2x
=2sin(2x-π/6)
当x∈[-π/12,π/2],(2x-π/6)∈[-π/3,5π/6],则f(x)∈[-√3,2]
于是-√3-m≤f(x)-m≤2-m
所以-√3-m>-2且2-m