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Problems
Contests
National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
2012 Vietnam National Olympiad
3
VMO 2012 P7
VMO 2012 P7
Source: VMO
January 12, 2012
function
limit
algebra proposed
algebra
Problem Statement
Find all
f
:
R
ā
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that: (a) For every real number
a
a
a
there exist real number
b
b
b
:
f
(
b
)
=
a
f(b)=a
f
(
b
)
=
a
(b) If
x
>
y
x>y
x
>
y
then
f
(
x
)
>
f
(
y
)
f(x)>f(y)
f
(
x
)
>
f
(
y
)
(c)
f
(
f
(
x
)
)
=
f
(
x
)
+
12
x
.
f(f(x))=f(x)+12x.
f
(
f
(
x
))
=
f
(
x
)
+
12
x
.
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