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Functional equation - Argentina TST 2010
Functional equation - Argentina TST 2010
Source:
May 2, 2010
function
limit
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb R \rightarrow \mathbb R
f
:
R
→
R
such that
f
(
x
+
x
y
+
f
(
y
)
)
=
(
f
(
x
)
+
1
2
)
(
f
(
y
)
+
1
2
)
f(x+xy+f(y)) = \left(f(x)+\frac{1}{2}\right) \left(f(y)+\frac{1}{2}\right)
f
(
x
+
x
y
+
f
(
y
))
=
(
f
(
x
)
+
2
1
)
(
f
(
y
)
+
2
1
)
holds for all real numbers
x
,
y
x,y
x
,
y
.
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