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Purple Comet Problems
2003 Purple Comet Problems
9
Problem 9, Fall 2003 , MS and HS
Problem 9, Fall 2003 , MS and HS
Source:
June 23, 2011
function
Problem Statement
Let
f
f
f
be a real-valued function of real and positive argument such that
f
(
x
)
+
3
x
f
(
1
x
)
=
2
(
x
+
1
)
f(x) + 3xf(\tfrac1x) = 2(x + 1)
f
(
x
)
+
3
x
f
(
x
1
)
=
2
(
x
+
1
)
for all real numbers
x
>
0
x > 0
x
>
0
. Find
f
(
2003
)
f(2003)
f
(
2003
)
.
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