函数f(x)对任意实数x满足f(x+2)=1/f(x),若f(1)=-5,f(f(5))等于?

f(1)=-5 f(3)=1/f(1)=-1/5f(5)=1/f(3)=-5f(1)=f(-1+2)=1/f(-1)=-5 得f(-1)=-1/5f(-1)=f(-3+2)=1/f(-3)=-1/5 得f(-3)=-5f(-3)=f(-5+2)=1/f(-5)=-5 得f(-5)=-1/5所以f(f(5))=-1/5