Solution:

$ \begin{array}{ll}\\ x(0)=4 & x(1)=5 \quad x(2)=0 \quad x(3)=7 \\\\ x(-1)=3 & x(-2)=2 \quad x(-3)=1\\ \end{array} $

$ \begin{aligned}\\ x(z) & =\sum_{n=-\infty}^{\infty} x(n) z^{-n} \\\\ & =\sum_{n=-3}^3 x(n) z^{-n}\\ \end{aligned} $

$ \begin{aligned}\\ & =x(-3) z^{+3}+x(-z) z^{+2}+x(-1) z^{+1}+x(0) z^0+ \\\\ & x(1) z^{-1}+x(2) z^{-2}+x(3) z^{-3}\\ \end{aligned}\\ $

$ =1 …