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National and Regional Contests
Singapore Contests
Singapore MO Open
2012 Singapore MO Open
2
Functional Equation
Functional Equation
Source: SMO 2012 Q2
June 30, 2012
function
algebra proposed
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
so that
(
x
+
y
)
(
f
(
x
)
−
f
(
y
)
)
=
(
x
−
y
)
f
(
x
+
y
)
(x+y)(f(x)-f(y))=(x-y)f(x+y)
(
x
+
y
)
(
f
(
x
)
−
f
(
y
))
=
(
x
−
y
)
f
(
x
+
y
)
for all
x
,
y
x,y
x
,
y
that belongs to
R
\mathbb{R}
R
.
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