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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 for all
x
,
y
,
∈
R
x,y, \in \mathbb{R}
x
,
y
,
∈
R
,
x
f
(
x
+
x
y
)
=
x
f
(
x
)
+
f
(
x
2
)
⋅
f
(
y
)
.
xf(x+xy)=xf(x)+f(x^{2})\cdot f(y).
x
f
(
x
+
x
y
)
=
x
f
(
x
)
+
f
(
x
2
)
⋅
f
(
y
)
.
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