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National and Regional Contests
Israel Contests
Israel Olympic Revenge
2023 Israel Olympic Revenge
P3
P3
Part of
2023 Israel Olympic Revenge
Problems
(1)
Same equation with different condition
Source: 2023 Israel Olympic Revenge P3
6/15/2023
Find all (weakly) increasing
f
:
R
→
R
f\colon \mathbb{R}\to \mathbb{R}
f
:
R
→
R
for which
f
(
f
(
x
)
+
y
)
=
f
(
f
(
y
)
+
x
)
f(f(x)+y)=f(f(y)+x)
f
(
f
(
x
)
+
y
)
=
f
(
f
(
y
)
+
x
)
holds for all
x
,
y
∈
R
x, y\in \mathbb{R}
x
,
y
∈
R
.
olympic revenge
functional equation
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