Explanation:
To find f(t), we need to take the inverse Laplace transform of 1/(s^2 - 4s + 5).
We can start by factoring the denominator of the Laplace transform:
1/(s^2 - 4s + 5) = 1/[(s - 2)^2 + 1^2]
We can recognize this as the Laplace transform of the function f(t) = e^2t * sin(t). Therefore,
ℒ^{-1} {1/(s^2 - 4s + 5)} = e^{2t} sin(t)
Thus, f(t) = e^{2t} sin(t).