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Baltic Way
1998 Baltic Way
7
Find all functions
Find all functions
Source: Baltic Way 1998
January 11, 2011
function
algebra
functional equation
algebra proposed
Problem Statement
Let
R
\mathbb{R}
R
be the set of all real numbers. Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
satisfying for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
the equation
f
(
x
)
+
f
(
y
)
=
f
(
f
(
x
)
f
(
y
)
)
f(x)+f(y)=f(f(x)f(y))
f
(
x
)
+
f
(
y
)
=
f
(
f
(
x
)
f
(
y
))
.
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