The Table of Laplace Transforms has:

`Lap^{:-1:}{(e^(-as))/s}=u(t-a)`

(There is no need to use Property (3) above.)

So

`Lap^{:-1:}{2/s(e^(-3s)-e^(-4s))}`

`=2[Lap^{:-1:}{(e^(-3s))/s}-Lap^{:-1:}{(e^(-4s))/s}]`

`=2[u(t-3)-u(t-4)]`

So the inverse Laplace Transform is given by:

`g(t) = 2(u(t − 3) − u(t − 4))`

The graph of `g(t)` is given by:

12345-10.511.52tg(t)Open image in a new page

Graph of `g(t) = 2(u(t − 3) − u(t − 4))`.

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