Question

Given the following functions F(s), find f(t).

F(s) = (s + 1) / ((s + 2)(s + 6)

Answer 1

To find f(t), we need to apply the inverse Laplace transform to the given function F(s). The function F(s) can be decomposed into partial fractions. Applying the inverse Laplace transform, we have f(t) = A * e^(-2t) + B * e^(-6t).

Step-by-step explanation:

To find f(t), we need to apply the inverse Laplace transform to the given function F(s).

The function F(s) can be decomposed into partial fractions as follows: F(s) = A/(s+2) + B/(s+6), where A and B are constants.

Applying the inverse Laplace transform, we have f(t) = A * e^(-2t) + B * e^(-6t).