f(x)=sin^2x+cos^2x+2sinxcosx+cos2x-1
=1+sin2x+cos2x-1
=sin2x+cos2x
=根号下2(sin(2x+π/4))
(1)最小正周期 T=2π/2=π
(2)-π/2<=2x+π/4<=π/2
-3π/4<=2x<=π/4
-3π/8<=x<=π/8
(3)x∈【π/4，3π/4】
2x+π/4∈【3π/4,7π/4】
当x=3π/2时，f(x)=-根号下2
当x=π/4时,f(x)=1
所以f(x)∈【-根号下2，1】
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