f(x)对于任意实数x满足f(x+2)=1/f(x),若f(1)=-5,则f(f(5))=

一楼答案是对的,而我是这样做的(只供参考)
f(x+2)=1/f(x),的充要条件是f(x)=f(4-x),即f(x)的周期为T=4.
f(1)=f(4-1)=f(3)=-5,
f(5)=f(8-3)=f(3)=-5,
f(f(5))=f(-5),
而,f(x+2)=1/f(x),
f(-1)=1/f(1)=-1/5,
f(-3)=1/f(-1)=-5,
f(-5)=1/f(-3)=-1/5.
则f(f(5))=f(-5)=-1/5.

f(3)=1/f(1)=-1/5,那么f(5)=1/f(3)=-5
又f(1)=1/f(-1)所以f(-1)=-1/5
f(-1)=1/f(-3)得f(-3)=-5
同理f(f(5))=f(-5)=1/f(-3)=-1/5