MathDB
Problems
Contests
National and Regional Contests
Mathlinks Contests.
MathLinks Contest 3rd
1
0341 functional 3rd edition Round 4 p1
0341 functional 3rd edition Round 4 p1
Source:
May 9, 2021
functional
algebra
3rd edition
Problem Statement
Find all functions
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
f : (0, +\infty) \to (0, +\infty)
f
:
(
0
,
+
∞
)
→
(
0
,
+
∞
)
which are increasing on
[
1
,
+
∞
)
[1, +\infty)
[
1
,
+
∞
)
and for all positive reals
a
,
b
,
c
a, b, c
a
,
b
,
c
they fulfill the following relation
f
(
a
b
)
f
(
b
c
)
f
(
c
a
)
=
f
(
a
2
b
2
c
2
)
+
f
(
a
2
)
+
f
(
b
2
)
+
f
(
c
2
)
f(ab)f(bc)f(ca)=f(a^2b^2c^2)+f(a^2)+f(b^2)+f(c^2)
f
(
ab
)
f
(
b
c
)
f
(
c
a
)
=
f
(
a
2
b
2
c
2
)
+
f
(
a
2
)
+
f
(
b
2
)
+
f
(
c
2
)
.
Back to Problems
View on AoPS