答：
f(x)=2sin(x+π/6)-2cosx
=2(sinxcosπ/6+cosxsinπ/6-cosx)
=2(sinxcosπ/6-cosxsinπ/6)
=2sin(x-π/6)
樓主,你要問(wèn)什么問(wèn)題?1)求函數(shù)對(duì)稱中心 2)把函數(shù)y=f(x)的圖像按向量m平移得到函數(shù)g(x)的圖像,若函數(shù)g(x)是偶函數(shù),寫出m的絕對(duì)值最小的向量m的坐標(biāo)1）f(x)=2sin(x-π/6)=0x-π/6=kπ所以：對(duì)稱中心x=kπ+π/6，k∈Z2）f(x)=2sin(x-π/6)平移后是偶函數(shù)，g(x)=2sin(x-π/6+m)當(dāng)m-π/6=-π/2即m=-π/3時(shí)，g(x)=2sin(x-π/2)=-2cosx為偶函數(shù)所以：向量m即是使得f(x)向右平移π/3個(gè)單位所以：向量m的坐標(biāo)為（π/3,0）