The document provides the solution to finding the inverse Laplace Transform of the function F(s) = e^-7s / ( s^2 + 2s + 1 + 1). By applying the inverse Laplace transform, the solution is found to be f (t) = e^(-t) sin t f(t+7), which shifts the original function f(t) by 7 units to the right.

1. Find the inverse Laplace Transform. Please show all work.
Solution
F(s) = e^-7s / ( s^2 + 2s + 1 + 1)
= e^(-7s) / [ ( s + 1)^2 + 1^2 ]
Applying inverse laplce transform we get
f (t) = f( t - ( -7) ) e^(-t) sin t
= e^(-t) sin t f(t+7)