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MAA AMC
AMC 12/AHSME
1982 AMC 12/AHSME
19
Absolute Value
Absolute Value
Source:
January 17, 2006
Problem Statement
Let
f
(
x
)
=
∣
x
−
2
∣
+
∣
x
−
4
∣
−
∣
2
x
−
6
∣
f(x)=|x-2|+|x-4|-|2x-6|
f
(
x
)
=
∣
x
−
2∣
+
∣
x
−
4∣
−
∣2
x
−
6∣
for
2
≤
x
≤
8
2 \leq x\leq 8
2
≤
x
≤
8
. The sum of the largest and smallest values of
f
(
x
)
f(x)
f
(
x
)
is
(A)
1
(B)
2
(C)
4
(D)
6
(E)
none of these
\textbf {(A) } 1 \qquad \textbf {(B) } 2 \qquad \textbf {(C) } 4 \qquad \textbf {(D) } 6 \qquad \textbf {(E) }\text{none of these}
(A)
1
(B)
2
(C)
4
(D)
6
(E)
none of these
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