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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
1998 Iran MO (3rd Round)
3
Functional Equation
Functional Equation
Source: Iran Third Round MO 1998, Exam 3, P3
October 31, 2010
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb R \to \mathbb R
f
:
R
→
R
such that for all
x
,
y
,
x, y,
x
,
y
,
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
f
(
x
)
y
.
f(f(x) + y) = f(x^2 - y) + 4f(x)y.
f
(
f
(
x
)
+
y
)
=
f
(
x
2
−
y
)
+
4
f
(
x
)
y
.
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