已知f(x)=2sin(2x-π/3)+1,x∈[π/4,π/2]若不等式丨f（x）-m丨＜2,在x∈[π/4,π/2]上恒成立,求实数m的取值范围

已知f(x)=2sin(2x-π/3)+1,x∈[π/4,π/2]若不等式丨f（x）-m丨＜2,在x∈[π/4,π/2]上恒成立,求实数m的取值范围
已知f(x)=2sin(2x-π/3)+1,x∈[π/4,π/2]
若不等式丨f（x）-m丨＜2,在x∈[π/4,π/2]上恒成立,求实数m的取值范围

已知f(x)=2sin(2x-π/3)+1,x∈[π/4,π/2]若不等式丨f（x）-m丨＜2,在x∈[π/4,π/2]上恒成立,求实数m的取值范围
f(x)=2sin(2x-π/3)+1,x∈[π/4,π/2]
∵ x∈[π/4,π/2]
∴ 2x-π/3∈[π/6,2π/3]
∴ sin(2x-π/3)∈[1/2,1]
∴ f(x)=2sin(2x-π/3)+1∈[2,3]
∵ |f(x)-m|