To compute the inverse Laplace transform of the function, we use L^(-1){f(s)} notation, and we have f(s) = s^3 + s^2 + 9s + 91.
First, let's break this down into smaller parts considering basic Laplace transforms. The function would become F(s) = L^(-1){s^3} + L^(-1){s^2} + L^(-1){9s} + L^(-1){91}.
The basic rules of inverse Laplace transforms and the linearity property suggest that we can calculate the inverse Laplace transform for each piece:
1. L^(-1){s^3} = t^2 * 2!
2. L^(-1){s^2} = t * 1!
3. L^(-1){9s} = 9
4. L^(-1){91} = 0, since the inverse Laplace transform of a constant is a delta function, but it will be 0 for t > 0.
Adding each part together, the inverse Laplace transform of the given function is f(t) = 2t^2 + t + 9.
A more complex approach would involve complex analysis and the residue theorem, but the above should provide a valid solution according to standard Laplace Transform tables.
Please note that while the solution is given in terms of standard Laplace transforms, individual results can vary depending on the specific properties and definitions used. It's always a good practice to check back your solutions with the original definitions to make sure everything aligns.