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Flanders Math Olympiad
2007 Flanders Math Olympiad
4
Functional equation
Functional equation
Source: 2007 Flanders Math Olympiad, Problem 4
April 26, 2015
national olympiad
functional equation
algebra
Problem Statement
If
f
,
g
:
R
→
R
f,g: \mathbb{R} \to \mathbb{R}
f
,
g
:
R
→
R
are functions that satisfy
f
(
x
+
g
(
y
)
)
=
2
x
+
y
f(x+g(y)) = 2x+y
f
(
x
+
g
(
y
))
=
2
x
+
y
∀
x
,
y
∈
R
\forall x,y \in \mathbb{R}
∀
x
,
y
∈
R
, then determine
g
(
x
+
f
(
y
)
)
g(x+f(y))
g
(
x
+
f
(
y
))
.
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