MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2020 Swedish Mathematical Competition
3
3
Part of
2020 Swedish Mathematical Competition
Problems
(1)
f (f (x) + y) = f (x) + f (y), bounded
Source: 2020 Swedish Mathematical Competition p3
5/1/2021
Determine all bounded functions
f
:
R
ā
R
f: R \to R
f
:
R
ā
R
, such that
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
f
(
y
)
f (f (x) + y) = f (x) + f (y)
f
(
f
(
x
)
+
y
)
=
f
(
x
)
+
f
(
y
)
, for all real
x
,
y
x, y
x
,
y
.
bounded
algebra
functional equation
functional
ISL