已知函数f(x)=sin(x/3)cos(x/3)+√3cos^2(x/3)

∵b^2=ac
由余弦定理b^2=a^2+c^2-2accosx
cosx=(a^2+c^2-ac)/(2ac)=(a^2+c^2)/(2ac)-1/2≥(2ac)/(2ac)-1/2=1/2
∴0≤x≤π/3 (1)
f(x)=sin(x/3)cos(x/3)+√3cos^2(x/3)
=sin(2x/3+π/3)+√3/2
f(x)max=1+√3/2
由(1)知 π/3≤2x/3+π/3≤5π/9
∴f(x)min=sin(π//3)+√3/2=√3
∴函数的值域为[√3,1+√3/2]