Question

函数y=tan(x-π/6)的定义域是？

Answer 1

解：2x+π/4≠kπ+π/2(k∈z)
所以x≠kπ/2+π/8(k∈z)
即函数y=tan(2x+π/4)的定义域是{x|x≠kπ/2+π/8(k∈z)}

Answer 2

y=tan(x-π/6)
=sin(x-π/6)/cos(x-π/6)
cos(x-π/6)≠0
x-π/6≠kπ+π/2
x≠kπ+2π/3
k是整数
所以函数y=tan(x-π/6)的定义域是x≠kπ+2π/3
k是整数

Answer 3

y=tan(x)的定义域是(-π/2+kπ,π/2+kπ)
y=tan(x-π/6)的定义域是x-π/6∈(-π/2+kπ,π/2+kπ),
所以定义域是x∈(-π/3+kπ,2π/3+kπ)，k是整数