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Iran Contests
Iran MO (3rd Round)
2002 Iran MO (3rd Round)
2
Function
Function
Source: Iranian National Olympiad (3rd Round) 2002
October 1, 2006
function
limit
algebra proposed
algebra
Problem Statement
f
:
R
⟶
R
+
f: \mathbb R\longrightarrow\mathbb R^{+}
f
:
R
⟶
R
+
is a non-decreasing function. Prove that there is a point
a
∈
R
a\in\mathbb R
a
∈
R
that
f
(
a
+
1
f
(
a
)
)
<
2
f
(
a
)
f(a+\frac1{f(a)})<2f(a)
f
(
a
+
f
(
a
)
1
)
<
2
f
(
a
)
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