Solving Inverse Laplace Transform: Understanding L^{-1}(8)

[manderz2112]

This might sound kinda dumb, but what is the Inverse Laplace transform of a number?

So L$$^{-1}$$(8) for example.

 

[matematikawan]

$$L^{-1}\{1\}=\delta(t)$$.
So I suspect $$L^{-1}\{8\}=8\delta(t)$$.

 

[I like Serena]

$$L^{-1}\{1\}=\delta(t)$$.
So I suspect $$L^{-1}\{8\}=8\delta(t)$$.

wolframalpha.com confirms with:

$$\mathcal{L}_t^{-1}[8](t) = 8 \delta(t)$$

http://www.wolframalpha.com/input/?i=InverseLaplaceTransform[8%2Cs%2Ct]

 

[JJacquelin]

This might sound kinda dumb, but what is the Inverse Laplace transform of a number?

The Inverse Laplace transform of a constant function is the Dirac delta function multiplied by the constant.
Strictly speaking it isn't the Laplace transform of a number, but the Laplace transform of a constant function which constant is equal to a number (in order to say that a function is something else that a number).