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。
1
f(x)=2sin(x/4)cos(x/4)-2√3sin²（x/4)+√3
f(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/2
x=2kπ+4π/3≠0
∴g(x)是非奇非偶函数
2
2kπ-π/2≤x/2-π/6≤2kπ+π/2
4kπ-2π/3≤x≤4kπ+4π/3
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