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EGMO
2012 EGMO
3
3
Part of
2012 EGMO
Problems
(1)
Find all real functions
Source: 2012 European Girls’ Mathematical Olympiad P3
4/12/2012
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
f
(
y
f
(
x
+
y
)
+
f
(
x
)
)
=
4
x
+
2
y
f
(
x
+
y
)
f\left( {yf(x + y) + f(x)} \right) = 4x + 2yf(x + y)
f
(
y
f
(
x
+
y
)
+
f
(
x
)
)
=
4
x
+
2
y
f
(
x
+
y
)
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.Netherlands (Birgit van Dalen)
function
algebra
functional equation
EGMO
EGMO 2012