Final answer:
The question requires the use of inverse Laplace transform techniques to find f(t) from F(s) = 320 / s²(s + 8), involving partial fractions decomposition and back-transforming each term.
Step-by-step explanation:
The question asks to find the function f(t) given the Laplace transform F(s) = 320 / s²(s + 8). This involves using inverse Laplace transform techniques to convert the function back into the time domain. To solve for f(t), we first decompose F(s) into partial fractions and then apply the inverse Laplace transform to each term separately. The partial fractions decomposition would typically result in terms like A/s and B/(s + 8). The corresponding f(t) would consist of terms that involve exponentials and powers of t. As this question does not involve specific numerical solutions, we cannot provide the exact form of f(t) without further calculations.