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6.47 Properties of the inverse Laplace transform

Theorem.

Let $F(s),G(s)$ be functions for which inverse Laplace transforms exist, and let $c$ be a constant. Then ${\mathcal{L}}^{-1}(F+G)={\mathcal{L}}^{-1}(F)+{\mathcal{L}}^{-1}(G)$ and ${\mathcal{L}}^{-1}(cF)=c{\mathcal{L}}^{-1}(F)$ .

This follows immediately from Theorem 6.40. (In terminology which you will see in MATH105, it can follows from the fact that ‘the inverse of an invertible linear map is a linear map’.)