Compute the z-transform for the discrete-time signalcompute

Question

1. Compute the z-Transform for the discrete-time signal.

2. Compute the inverse z-Transform of the transform X(z) = (4z +1) / (z² - z + .5)

3. A discrete-time system is give by the input/output difference equation y[n+2]-y[n+1]+y[n]=x[n+2]-x[n+1]. Is the system stable, marginally stable, or unstable?

4. Compute the pole for the transfer function H(z) = z / (z + 1)

5. A system has the transfer function H(z) = (z² - 3z +1) / (z³ + z² - 0.5z + 0.5).

Is the system stable, marginally stable, or unstable?