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Iran MO (2nd Round)
2022 Iran MO (2nd round)
2
2
Part of
2022 Iran MO (2nd round)
Problems
(1)
Functional equation
Source: Iran 2nd round 2022 P2
5/8/2022
Find all functions
f
:
R
ā
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
ā
R
such that for any real value of
x
,
y
x,y
x
,
y
we have:
f
(
x
f
(
y
)
+
f
(
x
)
+
y
)
=
x
y
+
f
(
x
)
+
f
(
y
)
f(xf(y)+f(x)+y)=xy+f(x)+f(y)
f
(
x
f
(
y
)
+
f
(
x
)
+
y
)
=
x
y
+
f
(
x
)
+
f
(
y
)
algebra
functional equation
function