Final answer:
The inverse Laplace transform of the function f(s) = s/(s² + s + 1) is found by completing the square in the denominator and using standard methods to obtain the time domain representation.
Step-by-step explanation:
The student is asking about the inverse Laplace transform of the function f(s) = \frac{s}{{s^2 + s + 1}}. The inverse Laplace transform is a mathematical process used to convert a function from the Laplace domain back to the time domain. To find the inverse, we can use a standard method that involves completing the square in the denominator and possibly using a Laplace transform table or known transform pairs. In this case, the denominator s^2 + s + 1 can be written as (s + \frac{1}{2})^2 + (\frac{\sqrt{3}}{2})^2 to complete the square. Then, we identify the inverse transform typically associated with the arctangent function or exponential decay, depending on the form after decomposition.