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2020-IMOC
A2
A nice fe
A nice fe
Source: IMOC 2020 A2
September 3, 2020
algebra
functional equation
function
IMOC
Problem Statement
Find all function
f
:
R
+
f:\mathbb{R}^+
f
:
R
+
→
R
+
\rightarrow \mathbb{R}^+
→
R
+
such that:
f
(
f
(
x
)
+
y
)
f
(
x
)
=
f
(
x
y
+
1
)
∀
x
,
y
∈
R
+
f(f(x) + y)f(x) = f(xy + 1) \forall x, y \in \mathbb{R}^+
f
(
f
(
x
)
+
y
)
f
(
x
)
=
f
(
x
y
+
1
)
∀
x
,
y
∈
R
+
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