已知函数f(x)=根号3sin（2x-pia/6)+2sin^2(x-pia/12),x∈,求使函数取得最大值的x的集合

f(x)=√3sin(2x-π/6) + 2sin²(x-π/12)=√3sin(2x-π/6)+1-cos(2x-π/6)=2sin[(2x-π/6)-π/6] + 1=2sin(2x-π/3) + 1使函数取得最大值即 2x-π/3 = 2kπ+π/2x ={x| kπ+5π/12,k∈Z}