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Iran MO (2nd Round)
2004 Iran MO (2nd round)
2
2
Part of
2004 Iran MO (2nd round)
Problems
(1)
Ascendant Function - Iran NMO 2004 (Second Round) - Problem2
Source:
9/24/2010
Let
f
:
R
≥
0
→
R
f:\mathbb{R}^{\geq 0}\to\mathbb{R}
f
:
R
≥
0
→
R
be a function such that
f
(
x
)
−
3
x
f(x)-3x
f
(
x
)
−
3
x
and
f
(
x
)
−
x
3
f(x)-x^3
f
(
x
)
−
x
3
are ascendant functions. Prove that
f
(
x
)
−
x
2
−
x
f(x)-x^2-x
f
(
x
)
−
x
2
−
x
is an ascendant function, too. (We call the function
g
(
x
)
g(x)
g
(
x
)
ascendant, when for every
x
≤
y
x\leq{y}
x
≤
y
we have
g
(
x
)
≤
g
(
y
)
g(x)\leq{g(y)}
g
(
x
)
≤
g
(
y
)
.)
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