We can see that this function is in the form of $F(s)=e^{-as}f(s)$, which is a shifted function in the s-domain. The inverse Laplace transform of such a function is $L^{-1}\{e^{-as}f(s)\}=u_a(t)f(t-a)$, where $u_a(t)$ is the unit step function.
Show more…