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Romania Team Selection Test
2001 Romania Team Selection Test
2
No function satisfies inequality
No function satisfies inequality
Source: Romanian TST 2001
January 16, 2011
function
inequalities
algebra unsolved
algebra
Problem Statement
Prove that there is no function
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f:(0,\infty )\rightarrow (0,\infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
such that
f
(
x
+
y
)
≥
f
(
x
)
+
y
f
(
f
(
x
)
)
f(x+y)\ge f(x)+yf(f(x))
f
(
x
+
y
)
≥
f
(
x
)
+
y
f
(
f
(
x
))
for every
x
,
y
∈
(
0
,
∞
)
x,y\in (0,\infty )
x
,
y
∈
(
0
,
∞
)
.
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