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3
Albania BMO TST Problem 3
Albania BMO TST Problem 3
Source:
April 1, 2017
function
algebra
Problem Statement
Find all functions
f
:
R
+
ā
R
+
f : \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}
f
:
R
+
ā
R
+
such that :
f
(
x
)
f
(
y
)
f
(
z
)
=
9
f
(
z
+
x
y
f
(
z
)
)
f(x)f(y)f(z)=9f(z+xyf(z))
f
(
x
)
f
(
y
)
f
(
z
)
=
9
f
(
z
+
x
y
f
(
z
))
, where
x
x
x
,
y
y
y
,
z
z
z
, are three positive real numbers.
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