f(x)=2sinx/4cosx/4+√3[1-2(sinx/4)^2]
=sin(x/2)+√3cos(x/2)
=2sin(x/2+π/3)
最小正周期T=2π/(1/2)=4π
f(x)最小值=-2 f(x)最大值=2
g(x)=2sin[(x+π/3)/2+π/3)=2sin(x/2+π/2)=2cos(x/2)
因g(-x)=2cos(-x/2)=2cos(x/2)=g(x)
所以g(x)是偶函数.