f(x)=

3

sinωxcosωx+cos2ωx

=

3

2

sin2ωx+

1+cos2ωx

2

=

sin(2ωx+

π

6

)+

1

2

．

∵f（x）的最小正周期为π，∴

2π

2ω

=π，∴ω=1

∴f(x)=sin(2x+

π

6

)+

1

2

，∵-

π

6

≤x≤

π

3

，

∴-

π

6

≤2x+

π

6

≤

5π

6

∴-

1

2

≤sin(2x+

π

6

)≤1，∴0≤f(x)≤

3

2