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2023 Romania National Olympiad
2
Romania NMO 2023 Grade 9 P2
Romania NMO 2023 Grade 9 P2
Source: Romania National Olympiad 2023
April 14, 2023
algebra
function
Problem Statement
Determine functions
f
:
R
→
R
,
f : \mathbb{R} \rightarrow \mathbb{R},
f
:
R
→
R
,
with property that
f
(
f
(
x
)
)
+
y
⋅
f
(
x
)
≤
x
+
x
⋅
f
(
f
(
y
)
)
,
f(f(x)) + y \cdot f(x) \le x + x \cdot f(f(y)),
f
(
f
(
x
))
+
y
⋅
f
(
x
)
≤
x
+
x
⋅
f
(
f
(
y
))
,
for every
x
x
x
and
y
y
y
are real numbers.
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