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Switzerland - Final Round
2014 Switzerland - Final Round
3
3
Part of
2014 Switzerland - Final Round
Problems
(1)
A functional equation
Source: Switzerland Math Olympiad, Final round 2014, P3
6/2/2014
Find all such functions
f
:
R
→
R
f :\mathbb{R}\to \mathbb{R}
f
:
R
→
R
such that for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
the following holds :
f
(
x
2
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
y
f
(
x
)
+
x
f
(
x
+
y
)
f(x^2)+f(xy)=f(x)f(y)+yf(x)+xf(x+y)
f
(
x
2
)
+
f
(
x
y
)
=
f
(
x
)
f
(
y
)
+
y
f
(
x
)
+
x
f
(
x
+
y
)
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