Find the inverse Laplace transformation of $\frac{e^{-s}}{s+2}$

Question

My question is: Find the function $f(t)$ that has the following Laplace transform $$F(s)=\dfrac{e^{-s}}{s+2}$$ Thanks .

my try:I have find this Find the inverse Laplace transformation of $\dfrac{s+1}{(s^2 + 1)(s^2 +4s+13)}$

Answer 1

If you have $$F(s)=\frac{1}{s+2}$$ The solution is easily $$f(t)=e^{-2t}$$ But,because you have a time translation: $$L\{f(t-a)\}=e^{-as}F(s)$$

The transform is $$f(t)=e^{-2(t-1)}$$

Answer 2

Hint: $\mathcal{L}\{u(t-a)\} = \dfrac{e^{-as}}{s}$ and thus by a shift theorem $\mathcal{L}\{e^{bt}u(t-a)\} = \dfrac{e^{-a(s-b)}}{s-b}$.