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Balkan MO Shortlist
2016 Balkan MO Shortlist
A6
A6
Part of
2016 Balkan MO Shortlist
Problems
(1)
f(f(x) + y) = f(x) + 3x + yf(y) , for x,y>0, f: (0,+\infty)\to(0,+\infty),
Source: Balkan BMO Shortlist 2016 A6
7/30/2019
Prove that there is no function from positive real numbers to itself,
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
f : (0,+\infty)\to(0,+\infty)
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
such that:
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
3
x
+
y
f
(
y
)
f(f(x) + y) = f(x) + 3x + yf(y)
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
3
x
+
y
f
(
y
)
,for every
x
,
y
∈
(
0
,
+
∞
)
x,y \in (0,+\infty)
x
,
y
∈
(
0
,
+
∞
)
by Greece, Athanasios Kontogeorgis (aka socrates)
functional equation
function
algebra
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