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2018 Poland - Second Round
1
1
Part of
2018 Poland - Second Round
Problems
(1)
Determine all functions
Source: 69 Polish MO 2018 Second Round - Problem 1
4/28/2018
Determine all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
which satisfy conditions:
f
(
x
)
+
f
(
y
)
≥
x
y
f(x) + f(y) \ge xy
f
(
x
)
+
f
(
y
)
≥
x
y
for all real
x
,
y
x, y
x
,
y
and for each real
x
x
x
exists real
y
y
y
, such that
f
(
x
)
+
f
(
y
)
=
x
y
f(x) + f(y) = xy
f
(
x
)
+
f
(
y
)
=
x
y
.
functional equation
algebra
Poland
function