已知函数f(x)=根号2sin(2x-π/4)+2,x∈[0,3π/4],则f(x)的值域为?

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已知函数f(x)=根号2sin(2x-π/4)+2,x∈[0,3π/4],则f(x)的值域为?

x∈[0,3π/4],2x∈[0,3π/2],2x-π/4∈[-π/4,π/2],在[-π/4,π/2]上f(x)为增函数,所以值域为[-π/2,√2](