已知函数fx=3tan(2x-π/3)已知函数f(x)=3tan(2x-π/3),求f(x)的定义域；比较f(π/2)与f(-π/8)的大小.

Question

已知函数fx=3tan(2x-π/3)
已知函数f(x)=3tan(2x-π/3),求f(x)的定义域；比较f(π/2)与f(-π/8)的大小.

Answer 1

(1) 由2x-π/3≠kπ+π/2 得 x≠kπ/2+5π/12,k∈Z
所以f(x)=3tan(2x-π/3)的定义域是{x∈R|x≠kπ/2+5π/12,k∈Z}
(2) f(π/2)=3tan(2(π/2)-π/3)=-3tan(π/3)0
所以f(π/2)