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Balkan MO Shortlist
2019 Balkan MO Shortlist
A2
A2
Part of
2019 Balkan MO Shortlist
Problems
(1)
f(xy) = yf(x) + x + f(f(y) - f(x))
Source: Shortlist BMO 2019, A2
11/7/2020
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
y
)
=
y
f
(
x
)
+
x
+
f
(
f
(
y
)
−
f
(
x
)
)
f(xy) = yf(x) + x + f(f(y) - f(x))
f
(
x
y
)
=
y
f
(
x
)
+
x
+
f
(
f
(
y
)
−
f
(
x
))
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
functional equation
algebra
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