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2001 IMC
5
IMC 2001 Problem 11
IMC 2001 Problem 11
Source: IMC 2001 Day 2 Problem 5
October 30, 2020
function
functional equation
Problem Statement
Prove that there is no function
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
with
f
(
0
)
>
0
f(0) >0
f
(
0
)
>
0
, and such that
f
(
x
+
y
)
≥
f
(
x
)
+
y
f
(
f
(
x
)
)
for all
x
,
y
∈
R
.
f(x+y) \geq f(x) +yf(f(x)) \text{ for all } x,y \in \mathbb{R}.
f
(
x
+
y
)
≥
f
(
x
)
+
y
f
(
f
(
x
))
for all
x
,
y
∈
R
.
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