MathDB
Problems
Contests
National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2004 Czech and Slovak Olympiad III A
6
a functional equation on positive reals
a functional equation on positive reals
Source: Czech and Slovak third round,2004,p6
March 3, 2012
function
algebra
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f:\mathbb R^+ \rightarrow \mathbb R^+
f
:
R
+
ā
R
+
such that for all positive real numbers
x
,
y
x,y
x
,
y
,
x
2
[
f
(
x
)
+
f
(
y
)
]
=
(
x
+
y
)
f
(
y
f
(
x
)
)
.
x^2[f(x)+f(y)]=(x+y)f(yf(x)).
x
2
[
f
(
x
)
+
f
(
y
)]
=
(
x
+
y
)
f
(
y
f
(
x
))
.
Back to Problems
View on AoPS