Find the \(z\)-transform of the following functions. The results of Problem 4.5-3 may be useful.

(a) \(E(s)=\frac{6 \varepsilon^{-0.3 T s}}{(s+1)(s+2)(s+3)}\)

(b) \(E(s)=\frac{4 \varepsilon^{-0.6 T s}}{s(s+2)^{2}}\)

(c) \(E(s)=\frac{s^{2}+2 s+2 \varepsilon^{-1.1 T s}}{s(s+2)^{2}}\)

(d) \(E(s)=\frac{(s+2)^{2} \varepsilon^{-0.2 T s}}{s^{2}(s+1)^{2}}\)

(e) \(E(s)=\frac{s^{2} \varepsilon^{-0.3 T s}+2 s+3}{s(s+2)^{2}(s+4)}\)

(f) \(E(s)=\frac{(2 s+7) \varepsilon^{-0.75 T s}}{\left(s^{2}+2 s+5ight)(s+3)}\)