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MAA AMC
AMC 12/AHSME
1993 AMC 12/AHSME
12
1993 AMC 12 #12 - Function
1993 AMC 12 #12 - Function
Source:
January 2, 2012
function
AMC
Problem Statement
If
f
(
2
x
)
=
2
2
+
x
f(2x)=\frac{2}{2+x}
f
(
2
x
)
=
2
+
x
2
for all
x
>
0
x>0
x
>
0
, then
2
f
(
x
)
=
2f(x)=
2
f
(
x
)
=
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
2
1
+
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
2
2
+
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
4
1
+
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
4
2
+
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
8
4
+
x
<span class='latex-bold'>(A)</span>\ \frac{2}{1+x} \qquad<span class='latex-bold'>(B)</span>\ \frac{2}{2+x} \qquad<span class='latex-bold'>(C)</span>\ \frac{4}{1+x} \qquad<span class='latex-bold'>(D)</span>\ \frac{4}{2+x} \qquad<span class='latex-bold'>(E)</span>\ \frac{8}{4+x}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
1
+
x
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
2
+
x
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
1
+
x
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
+
x
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
+
x
8
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