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2011 Morocco National Olympiad
3
Functional equation
Functional equation
Source: Morocco 2011
April 24, 2011
function
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algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
which verify the relation
(
x
−
2
)
f
(
y
)
+
f
(
y
+
2
f
(
x
)
)
=
f
(
x
+
y
f
(
x
)
)
,
∀
x
,
y
∈
R
.
(x-2)f(y)+f(y+2f(x))= f(x+yf(x)), \qquad \forall x,y \in \mathbb R.
(
x
−
2
)
f
(
y
)
+
f
(
y
+
2
f
(
x
))
=
f
(
x
+
y
f
(
x
))
,
∀
x
,
y
∈
R
.
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