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Switzerland - Final Round
2015 Switzerland - Final Round
3
Functional equation in real numbers
Functional equation in real numbers
Source: Swiss 2015
September 13, 2015
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
, such that for arbitrary
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
:
(
y
+
1
)
f
(
x
)
+
f
(
x
f
(
y
)
+
f
(
x
+
y
)
)
=
y
.
(y+1)f(x)+f(xf(y)+f(x+y))=y.
(
y
+
1
)
f
(
x
)
+
f
(
x
f
(
y
)
+
f
(
x
+
y
))
=
y
.
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