已知函数f(x)对任意实数x满足条件f(x+2)=1/f(x),若f(1)=-5,求f(f(5))的值
问题描述:
已知函数f(x)对任意实数x满足条件f(x+2)=1/f(x),若f(1)=-5,求f(f(5))的值
答
f(x+2)=1/f(x),
f(5)= f(3+2)=1/f(3) = 1/f(1+2) =1/[1/f(1)]=f(1)=-5
f(x)=1/f(x+2),
f(f(5))=f(-5)=1/f(-5+2)=1/f(-3)=f(-1)=1/f(1)=-1/5