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4
Functional Equation
Functional Equation
Source: Greek IMO TST 2010 Problem 4
August 17, 2014
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
∗
→
R
∗
f:\mathbb{R^{\ast }}\rightarrow \mathbb{ R^{\ast }}
f
:
R
∗
→
R
∗
satisfying
f
(
f
(
x
)
f
(
y
)
)
=
1
y
f
(
f
(
x
)
)
f(\frac{f(x)}{f(y)})=\frac{1}{y}f(f(x))
f
(
f
(
y
)
f
(
x
)
)
=
y
1
f
(
f
(
x
))
for all
x
,
y
∈
R
∗
x,y\in \mathbb{R^{\ast }}
x
,
y
∈
R
∗
and are strictly monotone in
(
0
,
+
∞
)
(0,+\infty )
(
0
,
+
∞
)
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