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AMC 12/AHSME
1980 AMC 12/AHSME
22
Maximum Value for Linear Equations
Maximum Value for Linear Equations
Source:
December 31, 2005
Problem Statement
For each real number
x
x
x
, let
f
(
x
)
f(x)
f
(
x
)
be the minimum of the numbers
4
x
+
1
4x+1
4
x
+
1
,
x
+
2
x+2
x
+
2
, and
−
2
x
+
4
-2x+4
−
2
x
+
4
. Then the maximum value of
f
(
x
)
f(x)
f
(
x
)
is
(A)
1
3
(B)
1
2
(C)
2
3
(D)
5
2
(E)
8
3
\text{(A)} \ \frac 13 \qquad \text{(B)} \ \frac 12 \qquad \text{(C)} \ \frac 23 \qquad \text{(D)} \ \frac 52 \qquad \text{(E)} \ \frac 83
(A)
3
1
(B)
2
1
(C)
3
2
(D)
2
5
(E)
3
8
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