已知函數(shù)f(x)=√3sin(wx+φ)+cos(wx+φ)(|φ|0)的最小正周期為π,且f(-x)=f(x),則下列關(guān)于g(x)=sin(wx+φ)的圖像說法正確的是（）
A.關(guān)于點(diǎn)（π/6,0）對稱B.關(guān)于直線x=π\(zhòng)12
C.在x∈[0,π/6]上,函數(shù)值域?yàn)閇0,1]D.函數(shù)在x∈[-π/4,π/3]上單調(diào)遞增
解析：∵函數(shù)f(x)=√3sin(wx+φ)+cos(wx+φ)(|φ|0)的最小正周期為π,且f(-x)=f(x)
∴f(x)=√3sin(wx+φ)+cos(wx+φ)=2sin(wx+φ+π/6)
∴f(x)=2sin(2x+φ+π/6)
∵f(-x)=f(x)
∴φ+π/6=π/2==>φ=π/3===>f(x)=2cos(2x)
∴g(x)=sin(2x+π/3)
g(π/6)=sin(π/3+π/3)=√3/2≠0==>A錯
2x+π/3=π/2==>2x=π/6==>x=π/12==>B正確