Answer
$e^{-t}(\cos t-3\sin t)$
Work Step by Step
Given: $F(s)=\frac{s-2}{s^2+2s+2}$
Using the Convolution Theorem
$L^{-1}[F(s)]=L^{-1}[\frac{s-2}{s^2+2s+2}]\\
=L^{-1}[\frac{s+1-3}{(s+1)^2+1}]\\
=e^{-t}L^{-1}[\frac{s-3}{s^2+1}]\\
=e^{-t}[L^{-1}(\frac{s}{s^2+1})-3L^{-1}(\frac{1}{s^2+1})]\\
=e^{-t}(\cos t-3\sin t)$
