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Romania Team Selection Test
2007 Romania Team Selection Test
2
functional inequality
functional inequality
Source: Romanian I TST 2007
April 13, 2007
inequalities
function
algebra proposed
algebra
Problem Statement
Let
f
:
Q
→
R
f: \mathbb{Q}\rightarrow \mathbb{R}
f
:
Q
→
R
be a function such that
∣
f
(
x
)
−
f
(
y
)
∣
≤
(
x
−
y
)
2
|f(x)-f(y)|\leq (x-y)^{2}
∣
f
(
x
)
−
f
(
y
)
∣
≤
(
x
−
y
)
2
for all
x
,
y
∈
Q
x,y \in\mathbb{Q}
x
,
y
∈
Q
. Prove that
f
f
f
is constant.
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