(Solved): Express \( f \) in terms of unit step functions. \[ \begin{array}{l} t \mathscr{U}(t-1)-(t-1)-\mat ...

Express \( f \) in terms of unit step functions. \[ \begin{array}{l} t \mathscr{U}(t-1)-(t-1)-\mathscr{U}(t-4) \\ t-1+\mathscr{U}(t-4) \\ t+\mathscr{U}(t-4) \\ t-(t-1) \mathscr{U}(t-1)-\mathscr{U}(t-4) \\ t+\mathscr{U}(t-1)-\mathscr{U}(t-4) \end{array} \] Find \( \mathscr{L}\{f(t)\} \) and \( \mathscr{L}\left\{e^{t} f(t)\right\} \). (Enter your answer in terms of s.) \[ \mathscr{L}\{f(t)\}= \] \[ \mathscr{L}\left\{e^{t} f(t)\right\}= \]