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2000 IMC
5
functional equation
functional equation
Source: IMC 2000 day 2 problem 5
October 29, 2005
function
algebra
domain
symmetry
real analysis
real analysis unsolved
Problem Statement
Find all functions
R
+
→
R
+
\mathbb{R}^+\rightarrow\mathbb{R}^+
R
+
→
R
+
for which we have for all
x
,
y
∈
R
+
x,y\in \mathbb{R}^+
x
,
y
∈
R
+
that
f
(
x
)
f
(
y
f
(
x
)
)
=
f
(
x
+
y
)
f(x)f(yf(x))=f(x+y)
f
(
x
)
f
(
y
f
(
x
))
=
f
(
x
+
y
)
.
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