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National and Regional Contests
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Latvia BW TST
2021 Latvia Baltic Way TST
P2
P2
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Functional inequality
Source: Latvian TST for Baltic Way 2021 P2
9/25/2021
Determine all functions
f
:
R
\
{
0
}
→
R
f: \mathbb{R} \backslash \{0 \} \rightarrow \mathbb{R}
f
:
R
\
{
0
}
→
R
such that, for all nonzero
x
x
x
:
f
(
1
x
)
≥
1
−
f
(
x
)
≥
x
2
f
(
x
)
f(\frac{1}{x}) \ge 1 -f(x) \ge x^2f(x)
f
(
x
1
)
≥
1
−
f
(
x
)
≥
x
2
f
(
x
)
inequalities