1. (2006 College Entrance Examination Mathematics (Anhui Science) Question) The function $f(x)$ satisfies the condition $f(x+2)=$ $\frac{1}{f(x)}$ for any $x$. If $f(1)=-5$, then the value of $f[f(5)]$ is
A. -5
B. 5
C. $-\frac{1}{5}$
D. $\frac{1}{5}$
1. C From $f(x+2)=\frac{1}{f(x)}$ we know that the function $f(x)$ is a periodic function with a period of 4, so $f(5)=f(1)=-5$, and $f(-1+2)=\frac{1}{f(-1)}$, thus $f[f(5)]=f(-5)=f(-1)=\frac{1}{f(1)}=-\frac{1}{5}$. Choose C.