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National and Regional Contests
Israel Contests
Israel Team Selection Test
2023 Israel TST
P1
Symmetric FE
Symmetric FE
Source: 2023 Israel TST Test 7 P1
May 9, 2023
TST
algebra
functional equation
function
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
→
R
such that for all
x
,
y
∈
R
x, y\in \mathbb{R}
x
,
y
∈
R
the following holds:
f
(
x
)
+
f
(
y
)
=
f
(
x
y
)
+
f
(
f
(
x
)
+
f
(
y
)
)
f(x)+f(y)=f(xy)+f(f(x)+f(y))
f
(
x
)
+
f
(
y
)
=
f
(
x
y
)
+
f
(
f
(
x
)
+
f
(
y
))
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