1.f(x)=2sin(2x+π/6).
2.x∈[π/12,π/2].
2x+π/6∈[π/3,7π/6].
sin(2x+π/6)∈[-1/2,1].
2sin(2x+π/6)∈[-1,2].所以:f(x)值域为:[-1,2].