MathDB
Problems
Contests
International Contests
Nordic
2022 Nordic
1
A functional equation
A functional equation
Source: 2022 Nordic Mathematical Olympiad
April 15, 2022
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
f
(
f
(
x
)
f
(
1
−
x
)
)
=
f
(
x
)
f(f(x)f(1-x))=f(x)
f
(
f
(
x
)
f
(
1
−
x
))
=
f
(
x
)
and
f
(
f
(
x
)
)
=
1
−
f
(
x
)
f(f(x))=1-f(x)
f
(
f
(
x
))
=
1
−
f
(
x
)
, for all real
x
x
x
.
Back to Problems
View on AoPS