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2022-IMOC
A6
A6
Part of
2022-IMOC
Problems
(1)
Hard positive real FE
Source: 2022 IMOC A6
9/5/2022
Find all functions
f
:
R
+
→
R
+
f:\mathbb R^+\to \mathbb R^+
f
:
R
+
→
R
+
such that
f
(
x
+
y
)
f
(
f
(
x
)
)
=
f
(
1
+
y
f
(
x
)
)
f(x+y)f(f(x))=f(1+yf(x))
f
(
x
+
y
)
f
(
f
(
x
))
=
f
(
1
+
y
f
(
x
))
for all
x
,
y
∈
R
+
.
x,y\in \mathbb R^+.
x
,
y
∈
R
+
.
Proposed by Ming Hsiao
algebra
functional equation