The correct answer is $\boxed{\text{A. }u(t) – 2e^{-t}u(t) + e^{-3t}u(t)}$.
The forced response of a system is the response of the system to a step input. The step input is a function that is zero for all time before $t=0$ and is equal to one for all time after $t=0$. The forced response of a system can be found by taking the Laplace transform of the step input and dividing by the Laplace transform of the system’s transfer function.
The Laplace transform of the step input is $1$. The Laplace transform of the system’s transfer function is $G(s) = \frac{3-s}{(s+1)(s+3)}$. Therefore, the forced response of the system is
$$Y_f(s) = \frac{1}{s} \cdot \frac{3-s}{(s+1)(s+3)} = \frac{3-s}{s(s+1)(s+3)}$$
We can find the forced response in the time domain by taking the inverse Laplace transform of $Y_f(s)$. The inverse Laplace transform of $\frac{3-s}{s(s+1)(s+3)}$ is
$$Y_f(t) = u(t) – 2e^{-t}u(t) + e^{-3t}u(t)$$
Therefore, the forced response of the system is $u(t) – 2e^{-t}u(t) + e^{-3t}u(t)$.
The other options are incorrect because they do not match the forced response of the system.