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Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2014 Dutch BxMO/EGMO TST
2
xf(xy)+f(-y)=xf(x)
xf(xy)+f(-y)=xf(x)
Source: Dutch BxMO/EGMO Team Selection Test 2014 P2
July 17, 2014
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
\
{
0
}
→
R
f:\mathbb{R}\backslash\{0\}\rightarrow\mathbb{R}
f
:
R
\
{
0
}
→
R
for which
x
f
(
x
y
)
+
f
(
−
y
)
=
x
f
(
x
)
xf(xy) + f(-y) = xf(x)
x
f
(
x
y
)
+
f
(
−
y
)
=
x
f
(
x
)
for all non-zero real numbers
x
,
y
x, y
x
,
y
.
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