I2.1 Given that functions $f(x)=x^{2}+r x+s$ and $g(x)=x^{2}-9 x+6$ have the properties that the sum of roots of $f(x)$ is the product of the roots of $g(x)$, and the product of roots of $f(x)$ is the sum of roots of $g(x)$. If $f(x)$ attains its minimum at $x=a$, find the value of $a$.
Let $\alpha, \beta$ be the roots of $f(x)$.
$$
\begin{array}{l}
\alpha+\beta=-r=6 ; \alpha \beta=s=9 \\
\therefore f(x)=x^{2}-6 x+9=(x-3)^{2}+0
\end{array}
$$
$f(x)$ attains the minimum value at $x=a=3$