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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2017 Switzerland - Final Round
2
2
Part of
2017 Switzerland - Final Round
Problems
(1)
f(x + yf(x)) = f(xf(y)) - x + f(y + f(x))
Source: Switzerland - 2017 Swiss MO Final Round p2
12/30/2022
Find all functions f :
R
→
R
R \to R
R
→
R
such that for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
:
f
(
x
+
y
f
(
x
)
)
=
f
(
x
f
(
y
)
)
−
x
+
f
(
y
+
f
(
x
)
)
.
f(x + yf(x)) = f(xf(y)) - x + f(y + f(x)).
f
(
x
+
y
f
(
x
))
=
f
(
x
f
(
y
))
−
x
+
f
(
y
+
f
(
x
))
.
algebra
functional
functional equation