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2016 Switzerland Team Selection Test
Problem 9
functional equation
functional equation
Source: Swiss IMO TST 2016. Problem 9
July 27, 2017
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
↦
R
f : \mathbb{R} \mapsto \mathbb{R}
f
:
R
↦
R
such that
(
f
(
x
)
+
y
)
(
f
(
x
−
y
)
+
1
)
=
f
(
f
(
x
f
(
x
+
1
)
)
−
y
f
(
y
−
1
)
)
\left(f(x)+y\right)\left(f(x-y)+1\right)=f\left(f(xf(x+1))-yf(y-1)\right)
(
f
(
x
)
+
y
)
(
f
(
x
−
y
)
+
1
)
=
f
(
f
(
x
f
(
x
+
1
))
−
y
f
(
y
−
1
)
)
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
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