Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want to do here is go the other way.

We are going to be specified a transform, F(s), and ask what function or say functions did we have originally. Since you will see it can be a more complicated and lengthy process than taking transforms. Under these cases we mean that we are determining the Inverse Laplace Transform of F(s) and use the subsequent notation.

f(t) = L ^-1{F(s)}  

Since with Laplace transforms, we've found the following fact to assist us take the inverse transform.

Fact

Specified the two Laplace transforms F(s) and G(s) after that,

L ^-1{aF(s) + bG(s)} = a L ^-1{F(s)} + b L ^-1{G(s)}

for any constants a and b.

Therefore, we take the inverse transform of the individual transforms, place any constants back in and after that subtract or add the results back up.