Question

已知定义在R上的奇函数f(x),满足f(x+2)=-f(x),求f(6)的值

Answer 1

f(x)是奇函数,f(0) = 0;

f(0) = f(-2+2)= -f(-2)=0;

f(-2)=0;

f(-2)=-f(2)=0;

f(2) = 0;

f(4)=f(2+2)=-f(2)=0;

f(6)=f(4+2)=-f(4)=f(4)=0;

所以f(6) = 0;