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Belarus Team Selection Test
2009 Belarus Team Selection Test
1
f(x-f(y))=xf(y)-yf(x)+g(x)
f(x-f(y))=xf(y)-yf(x)+g(x)
Source: 2009 Belarus TST 3.1
November 8, 2020
algebra
functional equation
functional
Problem Statement
Find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
and
g
:
R
→
R
g:R \to R
g
:
R
→
R
such that
f
(
x
−
f
(
y
)
)
=
x
f
(
y
)
−
y
f
(
x
)
+
g
(
x
)
f(x-f(y))=xf(y)-yf(x)+g(x)
f
(
x
−
f
(
y
))
=
x
f
(
y
)
−
y
f
(
x
)
+
g
(
x
)
for all real numbers
x
,
y
x,y
x
,
y
.I.Voronovich
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