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Switzerland Contests
Switzerland - Final Round
2005 Switzerland - Final Round
9
f(yf(x))(x + y) = x^2(f(x) + f(y))
f(yf(x))(x + y) = x^2(f(x) + f(y))
Source: Switzerland - 2005 Swiss MO Final Round p9
December 26, 2022
algebra
functional
functional equation
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f : R^+ \to R^+
f
:
R
+
ā
R
+
such that for all
x
,
y
>
0
x, y > 0
x
,
y
>
0
f
(
y
f
(
x
)
)
(
x
+
y
)
=
x
2
(
f
(
x
)
+
f
(
y
)
)
.
f(yf(x))(x + y) = x^2(f(x) + f(y)).
f
(
y
f
(
x
))
(
x
+
y
)
=
x
2
(
f
(
x
)
+
f
(
y
))
.
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