∵ 定义域是[π/24,π/2]
即 x∈[π/24,π/2]
∴ 2x-π/3∈[-π/4,2π/3]
∴ 2x-π/3=-π/4时,f(x)有最小值2*（-√2/2）=-√2
2x-π/3=π/2,f(x)有最小值2*1=2
∴ f(x)的值域是【-√2,2】