1.最小正周期为2π/2=π,
当2x+π/6∈(-π/2+2kπ,π/2+2kπ)时,函数单调递增,则增区间为x∈（-π/3+kπ,π/6+kπ)
当2x+π/6∈(π/2+2kπ,3π/2+2kπ)时,函数单调递减,则增区间为x∈（π/6+kπ,2π/3+kπ)
2.x∈(π/4,3π/4],2x+π/6∈(2π/3,5π/3],f(x)∈[-2,√3)
答：1.函数f(x)的最小正周期为π,x∈（-π/3+kπ,π/6+kπ)函数单调递增,x∈（π/6+kπ,2π/3+kπ) 函数单调递减.
2.f(x)的值域为[-2,√3).