Mathematics - Continuity - Differentiability Question with Solution | TestHub

Let$f : \mathrm{R}\to \mathrm{R}$satisfy the equation$f(x+y)=f\left(x\right)·f\left(y\right)$for all$x,y\in R$and$f\left(x\right)\ne 0$for any$x\in R$. If the function$f$is differentiable at$x=0$and$f^{\text{'}}\left(0\right)=3$, then$\underset{h\to 0}{\lim }\frac{1}{h}\left(f\left(h\right)-1\right)$is equal to ___ .