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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2002 Iran MO (3rd Round)
18
Another functional equation
Another functional equation
Source: Iran 2002
April 9, 2004
algebra proposed
algebra
Problem Statement
Find all continious
f
:
R
⟶
R
f: \mathbb R\longrightarrow\mathbb R
f
:
R
⟶
R
that for any
x
,
y
x,y
x
,
y
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
=
f
(
x
+
y
+
x
y
)
f(x)+f(y)+f(xy)=f(x+y+xy)
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
=
f
(
x
+
y
+
x
y
)
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