Question

已知f(x)满足f(x+3)=f(x),且f(x)是奇函数,f(1)=根号2,f(2006)=

Answer 1

由于f(x+3)=f(x)：

f(2006)=f(2003)=f(2000)=...=f(2) = f(-1)

又由于f(x)是奇函数,即f(-x)=-f(x)

f(2006)=f(-1)= - f(1) = - √2,