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Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2004 Switzerland - Final Round
4
4
Part of
2004 Switzerland - Final Round
Problems
(1)
f(xf(x) + f(y)) = y + f(x)^2
Source: Switzerland - 2004 Swiss MO Final Round p4
12/26/2022
Determine all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
holds
f
(
x
f
(
x
)
+
f
(
y
)
)
=
y
+
f
(
x
)
2
f(xf(x) + f(y)) = y + f(x)^2
f
(
x
f
(
x
)
+
f
(
y
))
=
y
+
f
(
x
)
2
algebra
functional
functional equation