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Problems
Contests
National and Regional Contests
Cuba Contests
Cuba MO
2005 Cuba MO
4
4
Part of
2005 Cuba MO
Problems
(1)
f(x)f(y) = f(xy) + 1/x + 1/y
Source: 2005 Cuba MO 2.4
9/15/2024
Determine all functions
f
:
R
+
→
R
f : R_+ \to R
f
:
R
+
→
R
such that:
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
1
x
+
1
y
f(x)f(y) = f(xy) + \frac{1}{x} + \frac{1}{y}
f
(
x
)
f
(
y
)
=
f
(
x
y
)
+
x
1
+
y
1
for all
x
,
y
x, y
x
,
y
positive reals.
algebra
functional