设函数f(x)=sin(wx+派／3)+sin(wx)（w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f

f(x)=sin(wx+π／3)+sin(wx)
=（3/2）sinwx+(√3/2）coswx
=√3sin(wx+π/6),
相邻两条对称轴间的距离为2,
∴π/w=2,w=π/2.
f(1)=3/2.
f(x+m)是偶函数,
f(x+m)=f(-x+m),
sin[(π/2)(x+m+1/3)]-sin[(π/2)(-x+m+1/3)]=0,
cos[(π/2)(m+1/3)]sin(πx/2)=0对任意x成立,
(π/2)(m+1/3)=(k+1/2)π,k∈Z,
m+1/3=2k+1,
∴正数m的最小值=2/3.