函数 (11 17:59:28)函数f(x)对任意实数x满足条件f(x+2)=1/f(x)若f(1)=-5 则f(f(5))=__

f(x+2)=1/f(x),f(x+4)=1/f(x+2)，将第二式代入一式有f(x)=f(x+4)，则很明显f(x)是周期为4的函数，则f(5)=f(1+4)=f(1)=-5,则f[f(5)]=f(-5)，令x=-1,f(1)=1/f(-1),则f(-1)=-1/5,f(-1)=f(-5+4)=f(-5)=-1/5故原复合函数为-1/5

f(x+2)=1/f(x)
f(3)=1/f(1)=-1/5
f(5)=1/f(3)=-5
f(f(5))=f(-5)
1/f(-5)=f(-3)=1/f(-1)=f(1)=5
f(f(5))=_5_

f(3)=1/f(1)=-1/5.
f(5)=1/f(3)=-5
f(x)=1/f(x+2)
f(f(5))=f(-5)=1/f(-3)=1/(1/f(-1))=f(-1)=1/f(1)=1/(1/f(3))=f(3)=-5

f(x+2)=1/f(x)
f(3)=1/f(1)=-1/5
f(5)=1/f(3)=-5
f(f(5))=f(-5)
1/f(-5)=f(-3)=1/f(-1)=f(1)=5
所以
f(f(5))=_5_