b$)$ The function $x[z]$ is given by:

$x[z]=\frac{4z^2-z}{z((z-3\mathrm{.}5)z+3\mathrm{.}5)-1}$

Based on the given equation,

$($i$)$ Determine the stability of the function $x[z]$ and justify your answer.

$(2$ marks$)$

$($ii$)$ Obtain the partial fraction of the $z-$transform, $x[z]$

$(8$ marks$)$

$($iii$)$ Find the inverse $z-$transform of $x(z)$ and sketch the ROC for the following:

a$)|z|<mn>0</mn><mn>.</mn><mn>5</mn>$

b$)|z|>2$

c