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2011 Armenian Republican Olympiads
Problem 1
Problem 1
Problem 1
Source: 2011 Armenian Republican Olympiad
August 1, 2016
function
algebra
Problem Statement
Does there exist a function
f
:
R
→
R
f\colon \mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that for any
x
>
y
,
x>y,
x
>
y
,
it satisfies
f
(
x
)
−
f
(
y
)
>
x
−
y
.
f(x)-f(y)>\sqrt{x-y}.
f
(
x
)
−
f
(
y
)
>
x
−
y
.
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