Mathematik-Online problems: Problem 121: Exponential Function

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	Mathematik-Online problems:
	Problem 121: Exponential Function

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The function $f:\mathbb{R}\longrightarrow\mathbb{R}$ shall have the properties

$\displaystyle f(x+y)$	$\displaystyle =$	$\displaystyle f(x)\cdot f(y), \qquad {\mbox{for all}} \ x, y\in\mathbb{R}\,,$	(1)
$\displaystyle f(0)$	$\displaystyle \neq$	$\displaystyle f(1).$	(2)

Show that

is true for all $r\in\mathbb{Q}\,,\, x\in\mathbb{R}$ .

Hint: Check at first the case $r\in\mathbb{N}$ .

(Authors: Kimmerle/Höfert)

see also:

automatisch erstellt am 14. 10. 2004