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Vietnam National Olympiad
2017 Vietnam National Olympiad
1
Problem 5 of VMO 2017
Problem 5 of VMO 2017
Source: Viet Nam National Olympiad 2017
January 6, 2017
function
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
satisfying relation :
f
(
x
f
(
y
)
−
f
(
x
)
)
=
2
f
(
x
)
+
x
y
f(xf(y)-f(x))=2f(x)+xy
f
(
x
f
(
y
)
−
f
(
x
))
=
2
f
(
x
)
+
x
y
∀
x
,
y
∈
R
\forall x,y \in \mathbb{R}
∀
x
,
y
∈
R
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