Give the inverse Laplace transform of
\(F(s) = \frac{4}{s^2} + \frac{2}{s} - \frac{2e^{-2s}}{s^2} - \frac{2e^{-2s}}{(s-2)^2}\)
a) \(f(x) = \begin{cases} 8x + 2, & 0 \le x < 2\\ 6x + 2 - 2(x - 2)e^{-4+2x}, & 2 \le x \end{cases}\)
\(f(x) = \begin{cases} 4x + 2, & 0 \le x < 2\\ 2x + 6 - 2(x - 2)e^{-4+2x}, & 2 \le x \end{cases}\)
\(f(x) = \begin{cases} 8x + 2, & 0 \le x < 2\\ 6x + 2 - 2e^{4+2x}, & 2 \le x \end{cases}\)
\(f(x) = \begin{cases} 4x + 2, & 0 \le x < 2\\ 2x + 6 - 2xe^{-4+2x}, & 2 \le x \end{cases}\)
\(f(x) = \begin{cases} 4x + 2, & 0 \le x < 2\\ 2x - 2 - 2xe^{2x}, & 2 \le x \end{cases}\)
None of the above.
