I know I can use the following: $\mathcal{L}^{-1}\{e^{-as}F(s)\} = u(t-a)f(t-a)$ $\mathcal{L}^{-1}\{\frac{n!}{s^{n+1}}\} = t^n$ $\mathcal{L}^{-1}\{F(s-a)\} = e^{at}f(t)$
but I'm confused as how to use them. In particular, for the first inverse above, if $a$ is negative, does that mean the equation becomes $u(t+a)f(t+a)$, or does the equation stay the same if we use the problem asked? If we have $e^{-3s}\frac{1}{(s-1)^2}$, why would it be
$u(t-3)(t-3)e^{t-3}$
as opposed to
$u(t+3)(t+3)e^{t+3}$
If, in this problem, the $a$ is negative?
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