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Korea National Olympiad
2014 Korea National Olympiad
2
easy functional equation
easy functional equation
Source: Korea National 2014 #2
January 21, 2015
function
algebra proposed
algebra
functional equation
KMO
Korea
Problem Statement
Determine all the functions
f
:
R
→
R
f : \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
that satisfies the following.
f
(
x
f
(
x
)
+
f
(
x
)
f
(
y
)
+
y
−
1
)
=
f
(
x
f
(
x
)
+
x
y
)
+
y
−
1
f(xf(x)+f(x)f(y)+y-1)=f(xf(x)+xy)+y-1
f
(
x
f
(
x
)
+
f
(
x
)
f
(
y
)
+
y
−
1
)
=
f
(
x
f
(
x
)
+
x
y
)
+
y
−
1
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