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Baltic Way
2012 Baltic Way
5
Functional Equation
Functional Equation
Source: 2012 Baltic Way, Problem 5
November 22, 2012
algebra
functional equation
Baltic Way
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
for which
f
(
x
+
y
)
=
f
(
x
−
y
)
+
f
(
f
(
1
−
x
y
)
)
f(x + y) = f(x - y) + f(f(1 - xy))
f
(
x
+
y
)
=
f
(
x
−
y
)
+
f
(
f
(
1
−
x
y
))
holds for all real numbers
x
x
x
and
y
y
y
.
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