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2008 Cuba MO
4
f(xy + f(x)) =xf(y) + f(x)
f(xy + f(x)) =xf(y) + f(x)
Source: 2008 Cube 2.4
August 27, 2024
algebra
functional
Problem Statement
Determine all functions
f
:
R
ā
R
f : R \to R
f
:
R
ā
R
such that
f
(
x
y
+
f
(
x
)
)
=
x
f
(
y
)
+
f
(
x
)
f(xy + f(x)) =xf(y) + f(x)
f
(
x
y
+
f
(
x
))
=
x
f
(
y
)
+
f
(
x
)
for all real numbers
x
,
y
x, y
x
,
y
.
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