Reverse of Laplace transform. Denoted as L−1{F(s)}\mathcal{L}^{-1} \{ F(s) \}L−1{F(s)}. L{f(t)}=F(s) ⟹ L−1{F(s)}=f(t)\mathcal{L}\{ f(t) \} = F(s) \implies \mathcal{L}^{-1} \{ F(s) \} = f(t) L{f(t)}=F(s)⟹L−1{F(s)}=f(t) Properties Basic Rule L−1{F(s+a)}=e−atf(t)L^{-1}\{F(s+a)\} = e^{-at}f(t) L−1{F(s+a)}=e−atf(t) Linearity L−1{cF(s)+G(s)}=cL−1{F(s)}+L−1{G(s)}\mathcal{L}^{-1} \{ cF(s) + G(s) \} = c\mathcal{L}^{-1}\{ F(s) \} + \mathcal{L}^{-1} \{ G(s) \} L−1{cF(s)+G(s)}=cL−1{F(s)}+L−1{G(s)} Time Shift L−1{e−asF(s)}=u(t−a)f(t−a)L^{-1}\{e^{-as}F(s)\}=u(t-a)f(t-a) L−1{e−asF(s)}=u(t−a)f(t−a) Scaling For α>0\alpha \gt 0α>0. L−1{F(αs)}=1αf(tα)L^{-1}\{F(\alpha s)\} = \frac{1}{\alpha} f\left(\frac{t}{\alpha}\right) L−1{F(αs)}=α1f(αt)