Final answer:
The question requires finding the time-domain function for the given Laplace-domain function s^3 / (s - 1). After expansion, the inverse transform can be determined using standard inverse Laplace transform pairs for each term.
Step-by-step explanation:
The question is asking to evaluate an inverse Laplace transform using the equation provided. Specifically, it requests finding the time-domain function corresponding to the Laplace-domain function L-1 { s3 / (s - 1) }.
First, we recognize that the function in the Laplace domain, s3 / (s - 1), can be expanded using polynomial division or partial fraction decomposition.
The result of this expansion will yield coefficients suitable for direct application of known inverse Laplace transforms. In the case of s3 / (s - 1), we realize that the function could be written as s2 + s1 + s0 + 1/(s - 1), which corresponds to time-domain functions involving exponential and polynomial terms, based on standard Laplace transform pairs.
Therefore, using the known inverse Laplace transforms for each term, we would find that L-1 { s3 / (s - 1) } is equivalent to a combination of exponentials and polynomial terms in the time domain. If the student required the full step-by-step evaluation, we would proceed to go through each term to find the resulting time function.