Question

函数f(x)对于任意实数x满足条件f(x+2)=1/f(x),若f(1)=-5求f(f(5))的值

Answer 1

因f(x+2)=1/f(x),可知f(x+4)=1/f(x+2),所以周期是4,则f(5)=f(1)=—5,所以f(f(5))=f(-5)代入f(x+2)=1/f(x),即得f(-5)=1/f(-3)=1/f(1)=-1/5