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Swedish Mathematical Competition
2004 Swedish Mathematical Competition
3
f(x)+x f(1-x) = x^2
f(x)+x f(1-x) = x^2
Source: Swedish Mathematical Competition 2004 p3
March 21, 2021
algebra
functional
functional equation
Problem Statement
A function
f
f
f
satisfies
f
(
x
)
+
x
f
(
1
ā
x
)
=
x
2
f(x)+x f(1-x) = x^2
f
(
x
)
+
x
f
(
1
ā
x
)
=
x
2
for all real
x
x
x
. Determine
f
f
f
.
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