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2012 Indonesia MO
2
2
Part of
2012 Indonesia MO
Problems
(1)
No such function exists
Source: Indonesia National Science Olympiad D2 P2
9/5/2012
Let
R
+
\mathbb{R}^+
R
+
be the set of all positive real numbers. Show that there is no function
f
:
R
+
→
R
+
f:\mathbb{R}^+ \to \mathbb{R}^+
f
:
R
+
→
R
+
satisfying
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
1
2012
f(x+y)=f(x)+f(y)+\dfrac{1}{2012}
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
+
2012
1
for all positive real numbers
x
x
x
and
y
y
y
.Proposer: Fajar Yuliawan
function
algebra proposed
algebra