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If $f:R\rightarrow R$ is such that $f(x+y)=f(x).f(y)$, then $f(0)$ = ?

$\begin{array}{1 1} 0 \\ 1\\ 0\;or\;1 \\ -1 \end{array}$

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Given : $f(x+y)=f(x).f(y)$
Put $ y=0$
$\Rightarrow\:f(x)=f(x).f(0)$
$\Rightarrow\:f(0)=1$
answered May 30, 2013 by rvidyagovindarajan_1
 

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