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Greece Team Selection Test
2017 Greece Team Selection Test
3
Functional equation with 2 fuctions
Functional equation with 2 fuctions
Source: Greece team selection test problem 3
May 3, 2017
algebra
functional equation
Problem Statement
Find all fuctions
f
,
g
:
R
→
R
f,g:\mathbb{R}\rightarrow \mathbb{R}
f
,
g
:
R
→
R
such that:
f
(
x
−
3
f
(
y
)
)
=
x
f
(
y
)
−
y
f
(
x
)
+
g
(
x
)
∀
x
,
y
∈
R
f(x-3f(y))=xf(y)-yf(x)+g(x) \forall x,y\in\mathbb{R}
f
(
x
−
3
f
(
y
))
=
x
f
(
y
)
−
y
f
(
x
)
+
g
(
x
)
∀
x
,
y
∈
R
and
g
(
1
)
=
−
8
g(1)=-8
g
(
1
)
=
−
8
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