In book signals and systems 2 edition a question is given which is as follows:
$$ x(t)=e^{-3(t+1)}u(t+1) $$
and we are asked to find the unilateral Laplace Transform of the signal. The method that is given in the solution manual is as follows:
Using Table 9.2 and time shifting property we get:
$$ X_2(s) = \frac{e^s}{s+3} $$
Now I am given a question which is as follows:
$$ e^{-2t}u(t-1) $$ and asked to find the Laplace Transform. Now can I apply the method as used above for unilateral Laplace Transform and get:
$$ \frac{e^{-s}}{s+2} \rightarrow A $$
Or does that method only holds true for unilateral Laplace Transforms? Because the answer marked A is wrong when I use this method. Also tell me when can I apply the property?