Determine an inverse Laplace transform of the given function

Determine an inverse Laplace transform of the given function.

Determine an inverse Laplace transform of the given function. e^-2s/s - 1

Solution

Using second shifting theorem

if L{f(t)} = F(s) then

L {f(t-a) u(t-a)} = e^-aS F(S)

By considering inverse of it

L^-1{e^-2s/s-1} = L^-1{1/s-1} _{t --> t-2}   (here t is shifted to t-2)

  L{e^at}= 1/s-a

L^-1{1/s-1}_{t --> t-2} = (e^t u(t))_{t --> t-2} = e^t-2u(t-2)