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2015 Middle European Mathematical Olympiad
2
f(x^2yf(x)) functional equation on nonzero reals
f(x^2yf(x)) functional equation on nonzero reals
Source: MEMO 2015, problem T-2
August 28, 2015
algebra
functional equation
Problem Statement
Determine all functions
f
:
R
∖
{
0
}
→
R
∖
{
0
}
f:\mathbb{R}\setminus\{0\}\to \mathbb{R}\setminus\{0\}
f
:
R
∖
{
0
}
→
R
∖
{
0
}
such that
f
(
x
2
y
f
(
x
)
)
+
f
(
1
)
=
x
2
f
(
x
)
+
f
(
y
)
f(x^2yf(x))+f(1)=x^2f(x)+f(y)
f
(
x
2
y
f
(
x
))
+
f
(
1
)
=
x
2
f
(
x
)
+
f
(
y
)
holds for all nonzero real numbers
x
x
x
and
y
y
y
.
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