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2011 Morocco National Olympiad
3
Functional equation Moroccan MO
Functional equation Moroccan MO
Source:
April 30, 2011
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that
∀
x
∈
R
f
(
x
)
=
m
a
x
(
2
x
y
−
f
(
y
)
)
\forall x\in \mathbb{R} \ \ f(x) = max(2xy-f(y))
∀
x
∈
R
f
(
x
)
=
ma
x
(
2
x
y
−
f
(
y
))
where
y
∈
R
y\in \mathbb{R}
y
∈
R
.
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