已知函数f(x)=2sin(x/4)cos(x/4)-2√3sin²（x/4)+√3,且g

已知函数f(x)=2sin(x/4)cos(x/4)-2√3sin²（x/4)+√3,且g

f(x)=sin(x/2) -√3[1-cos(x/2)]+√3=2[(1/2)sin(x/2) +(√3/2)cos(x/2)]=2sin(x/2+π/3)(1) g(x)=f(x+π/3)=2sin[(x+π/3)/2 +π/3)]=2sin(x/2 +π/2)=2cos(x/2)所以 g(x)是偶函数.(2)令 -π+2kπ≤x/2≤2kπ,得-2π+4kπ≤x≤4kπ,所以 增区间为[-2π+4kπ,4kπ],k是整数.======以下答案可供参考======供参考答案1:1f(x)=2sin(x/4)cos(x/4)-2√3sin²（x/4)+√3f(x)=2sin(x/4)cos(x/4)-√3(-2sin²（x/4)+1)=sin(x/2)-√3cos(x/2)=2sin(x/2-π/3)g(x)=2sin[(x+π/3)/2-π/3]=2sin(x/2-π/6)对称轴x/2-π/6=kπ+π/2x=2kπ+4π/3≠0∴g(x)是非奇非偶函数22kπ-π/2≤x/2-π/6≤2kπ+π/24kπ-2π/3≤x≤4kπ+4π/3

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