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2005 Slovenia Team Selection Test
2
x^2(f(x)+ f(y)) = (x+y)f (f(x)y) in R^+
x^2(f(x)+ f(y)) = (x+y)f (f(x)y) in R^+
Source: Slovenia TST 2005 p2
February 15, 2020
functional
functional equation
algebra
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f : R^+ \to R^+
f
:
R
+
ā
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 any
x
,
y
>
0
x,y > 0
x
,
y
>
0
.
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