Let f: R → R satisfy the equation f(x+y)=f(x). f(y) for all x, y ∈ R and f(x) ≠ 0 for any x ∈ R. If the function f is differentiable at x=0 and…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ satisfy the equation $\displaystyle f(x+y)=f(x) . f(y)$ for all $\displaystyle x, y \in \mathbf{R}$ and $\displaystyle f(x) \neq 0$ for any $\displaystyle x \in \mathbf{R}$. If the function $\displaystyle f$ is differentiable at $\displaystyle x=0$ and $\displaystyle f^{\prime}(0)=3$, then $\displaystyle \lim _{h \rightarrow 0} \frac{1}{h}(f(h)-1)$ is equal to \_\_\_\_.