13・11 Let $f(x)=|x-2|+|x-4|-|2 x-6|$, where $2 \leqslant x$ $\leqslant 8$, then the sum of the maximum and minimum values of $f(x)$ is
(A) 1 .
(B) 2 .
(C) 4 .
(D) 6 .
(E) None of the above values.
(33rd American High School Mathematics Examination, 1982)
[Solution] When $2 \leqslant x \leqslant 3$, $|x-2|=x-2,|x-4|=-(x-4)$,
$$
|2 x-6|=-(2 x-6),
$$

so at this time
$$
\begin{aligned}
f(x) & =(x-2)-(x-4)+(2 x-6) \\
& =-4+2 x,
\end{aligned}
$$

Similarly, when $3 \leqslant x \leqslant 4$,
$$
f(x)=(x-2)-(x-4)-(2 x-6)=8-2 x,
$$

When $4 \leqslant x \leqslant 8$,
$$
f(x)=(x-2)+(x-4)-(2 x-6)=0.
$$

Draw the graph of $f(x)$.
It is easy to see that $f(x)_{\max }=2, f(x)_{\min }=0$, the sum of which is 2. Therefore, the answer is $(B)$.