1. Given $f(x)=\frac{1+x}{2-x}$, define $f_{1}(x)=f(x), f_{n+1}(x)=f\left[f_{n}(x)\right]$, then the analytical expression of $f_{16}(x)$ is
A. $\frac{x+1}{x}$
B. $\frac{x}{x+1}$
C. $\frac{x}{x-1}$
D. $\frac{x-1}{x}$
1. $\mathrm{D}$ we get $f_{2}(x)=\frac{1}{1-x}, f_{3}(x)=\frac{2-x}{1-2 x}, f_{4}(x)=\frac{x-1}{x}, f_{5}(x)=\frac{2 x-1}{x+1}, f_{6}(x)=x$. $f_{7}(x)=f_{1}(x), \cdots, f_{16}(x)=f_{4}(x)=\frac{x-1}{x}$