Browse Questions

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

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

Given : $f(x+y)=f(x).f(y)$
Put $y=0$
$\Rightarrow\:f(x)=f(x).f(0)$
$\Rightarrow\:f(0)=1$