因为x∈[π/12,π/3]
2x∈[π/6,(2π)/3]
(2x+π/6)∈[π/3,(5π)/6]
所以1/2≤sin(2x+π/6）≤1
(根号2)/2≤ 根号2sin(2x+π/6）≤ 根号2
即f(x)的值域为 [(根号2)/2,根号2].