MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia National Math Olympiad
2014 Serbia National Math Olympiad
1
SMO 2014
SMO 2014
Source:
May 22, 2015
Olympiad
function
functional equation
Serbia
Problem Statement
Determine all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that for all
x
x
x
,
y
∈
R
y \in \mathbb{R}
y
∈
R
hold:
f
(
x
f
(
y
)
−
y
f
(
x
)
)
=
f
(
x
y
)
−
x
y
f(xf(y)-yf(x))=f(xy)-xy
f
(
x
f
(
y
)
−
y
f
(
x
))
=
f
(
x
y
)
−
x
y
Proposed by Dusan Djukic
Back to Problems
View on AoPS