作业帮已知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
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![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](/uploads/image/z/6934336-16-6.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3D2sin%282x-%CF%80%2F3%29%2B1%2Cx%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D%E8%8B%A5%E4%B8%8D%E7%AD%89%E5%BC%8F%E4%B8%A8f%EF%BC%88x%EF%BC%89-m%E4%B8%A8%EF%BC%9C2%2C%E5%9C%A8x%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D%E4%B8%8A%E6%81%92%E6%88%90%E7%AB%8B%2C%E6%B1%82%E5%AE%9E%E6%95%B0m%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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|