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2024 Kosovo Team Selection Test
P3
almost symmetric beautiful functional equation
almost symmetric beautiful functional equation
Source: Kosovo TST 2024 P3
March 19, 2024
Kosovo
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
such that
(
x
−
y
)
f
(
x
+
y
)
−
(
x
+
y
)
f
(
x
−
y
)
=
2
y
(
f
(
x
)
−
f
(
y
)
−
1
)
(x-y)f(x+y) - (x+y)f(x-y) = 2y(f(x)-f(y) - 1)
(
x
−
y
)
f
(
x
+
y
)
−
(
x
+
y
)
f
(
x
−
y
)
=
2
y
(
f
(
x
)
−
f
(
y
)
−
1
)
for all
x
,
y
∈
R
x, y\in\mathbb R
x
,
y
∈
R
.
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