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Azerbaijan Team Selection Test
2015 Azerbaijan IMO TST
2
2015 Azerbaijan IMO TST
2015 Azerbaijan IMO TST
Source: 2015 Azerbaijan IMO TST
May 29, 2015
algebra
function
Problem Statement
Find all functions
f
:
[
0
,
1
]
→
R
f:[0,1] \to \mathbb{R}
f
:
[
0
,
1
]
→
R
such that the inequality
(
x
−
y
)
2
≤
∣
f
(
x
)
−
f
(
y
)
∣
≤
∣
x
−
y
∣
(x-y)^2\leq|f(x) -f(y)|\leq|x-y|
(
x
−
y
)
2
≤
∣
f
(
x
)
−
f
(
y
)
∣
≤
∣
x
−
y
∣
is satisfied for all
x
,
y
∈
[
0
,
1
]
x,y\in [0,1]
x
,
y
∈
[
0
,
1
]
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