Final Answer:
The inverse Laplace transform of the given function (3s + 4) / (s² + 4s + 8) * 8 is 3e^(-2t)cos(2t) + 4e^(-2t)sin(2t).
Step-by-step explanation:
Given Function:
F(s) = (3s + 4) / (s² + 4s + 8) * 8.
Partial Fraction Decomposition:
F(s) = (A(s - 2) + Bs + C) / (s² + 4s + 8).
Solve for Constants A, B, C.
Inverse Laplace Transform of Partial Fractions:
f(t) = A e^(2t)cos(2t) + B e^(2t)sin(2t).
Multiply by 8:
f(t) = 3e^(-2t)cos(2t) + 4e^(-2t)sin(2t).
Therefore, the inverse Laplace transform is 3e^(-2t)cos(2t) + 4e^(-2t)sin(2t).