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Baltic Way
2014 Baltic Way
4
4
Part of
2014 Baltic Way
Problems
(1)
Functional equation
Source: Baltic Way 2014, Problem 4
11/11/2014
Find all functions
f
f
f
defined on all real numbers and taking real values such that
f
(
f
(
y
)
)
+
f
(
x
−
y
)
=
f
(
x
f
(
y
)
−
x
)
,
f(f(y)) + f(x - y) = f(xf(y) - x),
f
(
f
(
y
))
+
f
(
x
−
y
)
=
f
(
x
f
(
y
)
−
x
)
,
for all real numbers
x
,
y
.
x, y.
x
,
y
.
functional equation
algebra
Baltic Way