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Russian TST 2020
P1
Functional equation
Functional equation
Source: Russian TST 2020, Day 5 P1
March 21, 2023
algebra
functional equation
Problem Statement
Determine all functions
f
:
R
+
ā
R
+
f:\mathbb{R}^+\to\mathbb{R}^+
f
:
R
+
ā
R
+
satisfying
x
f
(
x
f
(
2
y
)
)
=
y
+
x
y
f
(
x
)
xf(xf(2y))=y+xyf(x)
x
f
(
x
f
(
2
y
))
=
y
+
x
y
f
(
x
)
for all
x
,
y
>
0
x,y>0
x
,
y
>
0
.
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