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2011 Belarus Team Selection Test
3
f(f(x+y))=xf(y)+g(x)
f(f(x+y))=xf(y)+g(x)
Source: 2011 Belarus TST 2.3
November 7, 2020
algebra
functional equation
functional
Problem Statement
Find all functions
f
:
R
→
R
,
g
:
R
→
R
f: R \to R ,g: R \to R
f
:
R
→
R
,
g
:
R
→
R
satisfying the following equality
f
(
f
(
x
+
y
)
)
=
x
f
(
y
)
+
g
(
x
)
f(f(x+y))=xf(y)+g(x)
f
(
f
(
x
+
y
))
=
x
f
(
y
)
+
g
(
x
)
for all real
x
x
x
and
y
y
y
.I. Gorodnin
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