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Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2010 Philippine MO
3
2010 Philippines MO P3
2010 Philippines MO P3
Source:
November 16, 2015
function
algebra
functional equation
PMO
2010
Problem Statement
Let
R
∗
\mathbb{R}^*
R
∗
be the set of all real numbers, except
1
1
1
. Find all functions
f
:
R
∗
→
R
f:\mathbb{R}^* \rightarrow \mathbb{R}
f
:
R
∗
→
R
that satisfy the functional equation
x
+
f
(
x
)
+
2
f
(
x
+
2009
x
−
1
)
=
2010
x+f(x)+2f\left(\frac{x+2009}{x-1}\right)=2010
x
+
f
(
x
)
+
2
f
(
x
−
1
x
+
2009
)
=
2010
.
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