The inputs x$($n$)$ and output y$($n$)$ of any caustic LTI system are as follows.

$($a$)$ Find the transfer function of the system. Mark the ROC clearly.

$($b$)$ Find the impulse response by applying the inverse z$-$transform to the transfer function of this system

$x(n)=(-\frac{1}{3}{)}^{n}u(n)$

$y(n)=3(-1{)}^{n}u(n)+(\frac{1}{3}{)}^{n}u(n)$

please sovle both of questions and show your detail steps. Thank you