求函数F(x)=tan(π/2x+π/3)的定义域和最小正周期

Question

求函数F(x)=tan(π/2x+π/3)的定义域和最小正周期

Answer 1

F(x)=tan(π/2x+π/3)
π/2x+π/3≠kπ+π/2
1/2x+1/3≠k+1/2
1/2x≠k+1/6
x≠2k+1/3,k∈Z
∴F(x)定义域为{x∈R|x≠2k+1/3,k∈Z}
F(x)最小正周期T=π/(π/2)=2