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Problems
Contests
National and Regional Contests
Iran Contests
Iran Team Selection Test
2024 Iran Team Selection Test
4
4
Part of
2024 Iran Team Selection Test
Problems
(1)
Classical FE
Source: Iran Team selection test 2024 - P4
5/19/2024
Find all functions
f
:
R
ā
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that for any real numbers
x
,
y
x , y
x
,
y
this equality holds :
f
(
y
f
(
x
)
+
f
(
x
)
f
(
y
)
)
=
x
f
(
y
)
+
f
(
x
y
)
f(yf(x)+f(x)f(y))=xf(y)+f(xy)
f
(
y
f
(
x
)
+
f
(
x
)
f
(
y
))
=
x
f
(
y
)
+
f
(
x
y
)
Proposed by Navid Safaei
algebra