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2011 Belarus Team Selection Test
3
f(x-f(x/y))=xf(1-f(1/y))
f(x-f(x/y))=xf(1-f(1/y))
Source: 2011 Belarus TST 7.3
November 7, 2020
algebra
functional
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:R\to R
f
:
R
→
R
such that for all real
x
,
y
x,y
x
,
y
with
y
≠
0
y\ne 0
y
=
0
f
(
x
−
f
(
x
/
y
)
)
=
x
f
(
1
−
f
(
1
/
y
)
)
f(x-f(x/y))=xf(1-f(1/y))
f
(
x
−
f
(
x
/
y
))
=
x
f
(
1
−
f
(
1/
y
))
and a)
f
(
1
−
f
(
1
)
)
≠
0
f(1-f(1))\ne 0
f
(
1
−
f
(
1
))
=
0
b)
f
(
1
−
f
(
1
)
)
=
0
f(1-f(1))= 0
f
(
1
−
f
(
1
))
=
0
S. Kuzmich, I.Voronovich
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