functional equations - $g(x+y)=g(x)g(y)$ for all $x,y inmathbb{R}$. If $g$ is continuous at $0$, prove that $g$ is continuous on $mathbb{R}$

$g(x+y)=g(x)g(y)$ for all $x,y \in\mathbb{R}$.

If $g$ is continuous at $0$, prove that $g$ is continuous on $\mathbb{R}$.