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Nordic
2016 Nordic
3
Nordic 2016 P3
Nordic 2016 P3
Source:
April 4, 2017
functional equation
function
Problem Statement
Find all
a
∈
R
a\in\mathbb R
a
∈
R
for which there exists a function
f
:
R
→
R
f\colon\mathbb R\rightarrow\mathbb R
f
:
R
→
R
, such that (i)
f
(
f
(
x
)
)
=
f
(
x
)
+
x
f(f(x))=f(x)+x
f
(
f
(
x
))
=
f
(
x
)
+
x
, for all
x
∈
R
x\in\mathbb R
x
∈
R
, (ii)
f
(
f
(
x
)
−
x
)
=
f
(
x
)
+
a
x
f(f(x)-x)=f(x)+ax
f
(
f
(
x
)
−
x
)
=
f
(
x
)
+
a
x
, for all
x
∈
R
x\in\mathbb R
x
∈
R
.
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