Question

函数f(x)是周期兀的偶函数,且当x=【0,兀】时,f(x)=√3tanx-1,则f(8兀/3)的值为

Answer 1

∵函数f(x)是周期兀的偶函数,∴f(x+π)=f(x)

∴f(8π/3)=f(-π/3),又因为f(x)是偶函数,所以f(-π/3)=f(π/3)

π/3属于[0,π],代入f(x)=√3tanx-1得：

f(8π/3)=f(π/3)=3-1=2

说明：其实这道题目有问题,因为还有一个答案是-4,同样满足题目本身要求,题目本身有漏洞