16.9. Provide an example of a rational function $R(x)$ (i.e., the ratio of two polynomials), which is different from a constant and satisfies $R(x)=R(1 / x)$ and $R(x)=R(1-x)$.
16.9. By replacing $x$ with $1-x$ and $1 / x$, from each number one can obtain a total of six different numbers: $x, 1 / x, 1-x, \frac{1}{1-x}, \frac{x}{x-1}$, $\frac{x-1}{x}$. Therefore, the function

$$
R(x)=x^{2}+\frac{1}{x^{2}}+(1-x)^{2}+\frac{1}{(1-x)^{2}}+\frac{x^{2}}{(1-x)^{2}}+\frac{(x-1)^{2}}{x^{2}}
$$

has the required properties.