函数f（X）=sin2x+2根号2cos（π/4+x）+3的值域.

f（X）=sin2x+2√2cos（π/4+x）+3
=cos(2x-π/2)+2√2cos（π/4+x）+3
=1-2sin²(x-π/4)-2√2sin（x-π/4）+3
=4-2(sin²(x-π/4)+√2sin（x-π/4))
=5-2(sin（x-π/4)+√2/2)²
值域y∈[2-2√2,5]