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2
Well known functional equation
Well known functional equation
Source: Argentina IMO 2005 TST, problem 2
April 28, 2005
function
algebra
functional equation
algebra proposed
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
∀
x
,
y
∈
R
\forall x,y \in \mathbb{R}
∀
x
,
y
∈
R
we have
f
(
x
f
(
x
)
+
f
(
y
)
)
=
f
(
x
)
2
+
y
f(xf(x)+f(y)) = f(x)^2 + y
f
(
x
f
(
x
)
+
f
(
y
))
=
f
(
x
)
2
+
y
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