Let f(x)=|x-2|+|x-4| -|2x-6|, for 2≤ x≤8. The sum of the largest and smallest values of f(x) is

1982 AMC 12 Problem 19

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19.

Let

f(x)=|x-2|+|x-4|

-|2x-6|,

for

2\le x\le8.

The sum of the largest and smallest values of

f(x)

1

2

4

6

none of these

Break the interval at the zeros

2,

3,

and

4

Simplify

f(x)

on each resulting interval

[2,3],

f(x)=2x-4;

[3,4],

f(x)=8-2x;

and on

[4,8],

f(x)=0.

Thus the minimum is

0

and the maximum is

2,

whose sum is

2.

Therefore, the correct answer is B.