MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2018 Swedish Mathematical Competition
2
2
Part of
2018 Swedish Mathematical Competition
Problems
(1)
f (x) + 2f (\sqrt[3]{1-x^3}) = x^3
Source: 2018 Swedish Mathematical Competition p2
5/1/2021
Find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
that satisfy
f
(
x
)
+
2
f
(
1
−
x
3
3
)
=
x
3
f (x) + 2f (\sqrt[3]{1-x^3}) = x^3
f
(
x
)
+
2
f
(
3
1
−
x
3
)
=
x
3
for all real
x
x
x
. (Here
x
3
\sqrt[3]{x}
3
x
is defined all over
R
R
R
.)
algebra
functional equation
functional