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Cuba MO
2007 Cuba MO
4
x^2(f(x)+f(y)) = (x+y)f(f(x)y)
x^2(f(x)+f(y)) = (x+y)f(f(x)y)
Source: 2007 Cuba MO 2.4
September 15, 2024
algebra
functional
functional equation
Problem Statement
Find all functions
f
:
R
+
→
R
+
f : R_+ \to R_+
f
:
R
+
→
R
+
such that
x
2
(
f
(
x
)
+
f
(
y
)
)
=
(
x
+
y
)
f
(
f
(
x
)
y
)
x^2(f(x)+f(y)) = (x+y)f(f(x)y)
x
2
(
f
(
x
)
+
f
(
y
))
=
(
x
+
y
)
f
(
f
(
x
)
y
)
for all positive real
x
,
y
x, y
x
,
y
.
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