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National and Regional Contests
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Spain Mathematical Olympiad
2012 Spain Mathematical Olympiad
2
Spanish functional equation
Spanish functional equation
Source: Spanish MO 2012 Q2
June 7, 2012
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that
(
x
−
2
)
f
(
y
)
+
f
(
y
+
2
f
(
x
)
)
=
f
(
x
+
y
f
(
x
)
)
(x-2)f(y)+f(y+2f(x))=f(x+yf(x))
(
x
−
2
)
f
(
y
)
+
f
(
y
+
2
f
(
x
))
=
f
(
x
+
y
f
(
x
))
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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