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Korea Winter Program Practice Test
2021 Korea Winter Program Practice Test
2
function
function
Source: 2021 Korea Winter Program Practice Test
February 8, 2021
function
algebra
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f:R^+\rightarrow R^+
f
:
R
+
ā
R
+
such that for all positive reals
x
x
x
and
y
y
y
4
f
(
x
+
y
f
(
x
)
)
=
f
(
x
)
f
(
2
y
)
4f(x+yf(x))=f(x)f(2y)
4
f
(
x
+
y
f
(
x
))
=
f
(
x
)
f
(
2
y
)
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