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Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2023-IMOC
A4
A4
Part of
2023-IMOC
Problems
(1)
Another Taiwan R+ FE
Source: IMOC 2023 A4
9/9/2023
Find all functions
f
:
R
+
ā
R
+
f:\mathbb{R^{+}} \rightarrow \mathbb{R^{+}}
f
:
R
+
ā
R
+
, such that
x
f
(
1
+
x
f
(
y
)
)
=
f
(
f
(
x
)
+
f
(
y
)
)
xf(1+xf(y))=f(f(x)+f(y))
x
f
(
1
+
x
f
(
y
))
=
f
(
f
(
x
)
+
f
(
y
))
for all positive reals
x
,
y
x, y
x
,
y
.
algebra