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National and Regional Contests
PEN Problems
PEN K Problems
23
23
Part of
PEN K Problems
Problems
(1)
K 23
Source:
5/25/2007
Let
Q
+
{\mathbb Q}^{+}
Q
+
be the set of positive rational numbers. Construct a function
f
:
Q
+
→
Q
+
f:{\mathbb Q}^{+}\rightarrow{\mathbb Q}^{+}
f
:
Q
+
→
Q
+
such that
f
(
x
f
(
y
)
)
=
f
(
x
)
y
f(xf(y)) = \frac{f(x)}{y}
f
(
x
f
(
y
))
=
y
f
(
x
)
for all
x
,
y
∈
Q
+
x, y \in{\mathbb Q}^{+}
x
,
y
∈
Q
+
.
function
Functional Equations