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2001 AIME Problems
8
A Certain Function
A Certain Function
Source:
December 28, 2006
function
analytic geometry
graphing lines
slope
symmetry
Problem Statement
A certain function
f
f
f
has the properties that
f
(
3
x
)
=
3
f
(
x
)
f(3x)=3f(x)
f
(
3
x
)
=
3
f
(
x
)
for all positive real values of
x
x
x
, and that
f
(
x
)
=
1
−
∣
x
−
2
∣
f(x)=1-\mid x-2 \mid
f
(
x
)
=
1
−
∣
x
−
2
∣
for
1
≤
x
≤
3
1\leq x \leq 3
1
≤
x
≤
3
. Find the smallest
x
x
x
for which
f
(
x
)
=
f
(
2001
)
f(x)=f(2001)
f
(
x
)
=
f
(
2001
)
.
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