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2023 USAMO
2
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Source: USAMO 2023/2
March 23, 2023
AMC
USA(J)MO
USAMO
functional equation
Problem Statement
Let
R
+
\mathbb{R}^+
R
+
be the set of positive real numbers. Find all functions
f
:
R
+
→
R
+
f \colon \mathbb{R}^+ \to \mathbb{R}^+
f
:
R
+
→
R
+
such that, for all
x
,
y
∈
R
+
x,y \in \mathbb{R}^+
x
,
y
∈
R
+
,
f
(
x
y
+
f
(
x
)
)
=
x
f
(
y
)
+
2.
f(xy+f(x))=xf(y)+2.
f
(
x
y
+
f
(
x
))
=
x
f
(
y
)
+
2.
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