(a) Show that, if x(t)is an even function, so that x(t) = x(—t), then X(s) = X(-s) (b)...

(a) Show that, if x(t)is an even function, so that x(t) = x(—t), then X(s) = X(-s)

(b) Show that, if x(t) is an odd function, so that x(t) = —x(-t), then X(s) = —X(--s).

(c) Determine which, if any, of the pole-zero plots in Figure P9.41 could corresponding to an even function of time. For those that could, indicate the required ROC.