已知函数f（x）=2cos方x+2sinxcosx．记函数g(x)=f(x)*f(x+π/4) 求g(x)值域

f(x)=2(cosx)^2+2sinxcosx=(cos2x+1)+sin2x=cos2x+sin2x+1
f(x+π/4)=cos(2x+π//2)+sin(2x+π//2)+1=sin2x-cos2x+1
g(x)=f(x)*f(x+π/4)=[cos2x+sin2x+1][sin2x-cos2x+1]=(sin2x+1)^2-(cos2x)^2
=(sin2x+1)^2-[1-(sin2x)^2]=2*(sin2x)^2-2sin2x-1=2(sin2x-1/2)^2-1/2
sin2x∈[-1,1] sin2x-1/2∈[-3/2,1/2]
g(x)∈[-1/2,4] g(x)的值域为[-1/2,4]

f(x)＝2(cosx)^2＋2sinxcosx
＝2(cosx)^2－1＋sin2x＋1
＝cos2x＋sin2x＋1
f(x＋π/4)＝cos[2(x＋π/4)]＋sin[2(x＋π/4)]＋1
＝－sin2x＋cos2x＋1
∴g(x)＝f(x)·f(x＋π/4)
＝(cos2x＋sin2x＋1)(－sin2x＋cos2x＋1)
＝(c...