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Old functional equation

Source: German TST 2004, Exam V, Problem 2

May 1, 2004

functionalgebra proposedalgebraFunctional EquationsGermanyTSTTeam Selection Test

Problem Statement

Find all functions

f: \Bbb{R}_{0}^{+}\rightarrow \Bbb{R}_{0}^{+}

with the following properties:
(a) We have

f\left( xf\left( y\right) \right) \cdot f\left( y\right) =f\left( x+y\right)

for all

x

and

y

. (b) We have

f\left(2\right) = 0

. (c) For every

x

with

0 < x < 2

, the value

f\left(x\right)

doesn't equal

0

.
NOTE. We denote by

\Bbb{R}_{0}^{+}

the set of all non-negative real numbers.

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