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China Contests
China Team Selection Test
2003 China Team Selection Test
2
Functional equation
Functional equation
Source: China TST 2003
June 29, 2006
function
algebra
functional equation
algebra unsolved
Problem Statement
Find all functions
f
,
g
f,g
f
,
g
:
R
→
R
R \to R
R
→
R
such that
f
(
x
+
y
g
(
x
)
)
=
g
(
x
)
+
x
f
(
y
)
f(x+yg(x))=g(x)+xf(y)
f
(
x
+
y
g
(
x
))
=
g
(
x
)
+
x
f
(
y
)
for
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
.
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