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National and Regional Contests
Netherlands Contests
Dutch IMO TST
2012 Dutch IMO TST
5
f(x + xy + f(y))=(f(x) + 1/2)(f(y) +1/2)
f(x + xy + f(y))=(f(x) + 1/2)(f(y) +1/2)
Source: Dutch IMO TST2 2012 p5
January 10, 2020
functional equation
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
satisfying
f
(
x
+
x
y
+
f
(
y
)
)
=
(
f
(
x
)
+
1
2
)
(
f
(
y
)
+
1
2
)
f(x + xy + f(y))=(f(x) + \frac12)(f(y) + \frac12 )
f
(
x
+
x
y
+
f
(
y
))
=
(
f
(
x
)
+
2
1
)
(
f
(
y
)
+
2
1
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
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