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Problems
Contests
National and Regional Contests
Iran Contests
Iran RMM TST
2021 Iran RMM TST
2
easy function on Tst
easy function on Tst
Source: Iranian RMM TST 2021 Day1 P2
April 16, 2021
function
algebra
Problem Statement
Let
f
:
R
+
→
R
f : \mathbb{R}^+\to\mathbb{R}
f
:
R
+
→
R
satisfying
f
(
x
)
=
f
(
x
+
2
)
+
2
f
(
x
2
+
2
x
)
f(x)=f(x+2)+2f(x^2+2x)
f
(
x
)
=
f
(
x
+
2
)
+
2
f
(
x
2
+
2
x
)
. Prove that if for all
x
>
140
0
2021
x>1400^{2021}
x
>
140
0
2021
,
x
f
(
x
)
≤
2021
xf(x) \le 2021
x
f
(
x
)
≤
2021
, then
x
f
(
x
)
≤
2021
xf(x) \le 2021
x
f
(
x
)
≤
2021
for all
x
∈
R
+
x \in \mathbb {R}^+
x
∈
R
+
Proposed by Navid Safaei
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