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2
Non-decreasing function [Iran TST 2010]
Non-decreasing function [Iran TST 2010]
Source:
June 9, 2010
function
inequalities
algebra proposed
algebra
Problem Statement
Find all non-decreasing functions
f
:
R
+
∪
{
0
}
→
R
+
∪
{
0
}
f:\mathbb R^+\cup\{0\}\rightarrow\mathbb R^+\cup\{0\}
f
:
R
+
∪
{
0
}
→
R
+
∪
{
0
}
such that for each
x
,
y
∈
R
+
∪
{
0
}
x,y\in \mathbb R^+\cup\{0\}
x
,
y
∈
R
+
∪
{
0
}
f
(
x
+
f
(
x
)
2
+
y
)
=
2
x
−
f
(
x
)
+
f
(
f
(
y
)
)
.
f\left(\frac{x+f(x)}2+y\right)=2x-f(x)+f(f(y)).
f
(
2
x
+
f
(
x
)
+
y
)
=
2
x
−
f
(
x
)
+
f
(
f
(
y
))
.
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