Use any method to determine the inverse z transform for the following function:

X(z) = (z^3-2*z)/((z-2)

- left sided sequence

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Please help me with these problems.
section 7.4 6,16,20,24
Samples of these questions appear below. Please see the attached files for the fully formatted problems.
Find the inverse Laplace transformation.
Determine Partial Fraction Expansions for the given rational function.
Determine L^-1{F}.

** Please see the attached file for the full problem description **
I want someone to show me the calculations and explain where necessary. Thanks in advance.
1) (i) Write down the equation of the line in xy-coordinates defined by
| z - (i + 1) | = | z + 2i |.
(ii) The LFT w = 1/z takes the line in (i) to a

I've attached a problem set which contains the following questions related to inverse functions. Can you help explain the concepts to me?
Given point P of the function f(x), state the corresponding point P' in the inverse of the function.
Determine if the inverse of each relation graphed below is a function.
Find the inver

1a.)Is y=x^4 a single- or multi-valued function?
b.)Is y=f(x)=x^2+4x an even, odd, or neither
function?
c.)What is the inverse function of y=x^4
d.)What is the inverse function of (b.),y=x^2+4x?
e.)Is the inverse function from (d.), odd, even, or
neither?

F(x) = 2x^2 - 8x, where x = or > 2
Even though I know that this particular quadratic equation does have an inverse since the domain is limited, I don't know how to figure out the formula for the inverse for a quadratic equation. I don't know how to solve for x, since there are two different x's.
Thank you!

Which functions are one-to-one? Which functions are onto? Describe the inverse function
A)F:Z^2-N where f is f(x,y) x^2 +2y^2
B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd)
C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd)
D)h:N^3 -> N where h(x,y,z) = x + y -z

1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D.
2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).

Define the unit ramp function by
...
1. Determine the Laplace transform of H(t)
2. Use the Laplace transform to solve the ODE
.....
Questions:
1. To determine the Laplace transform, do we use
.....
∫ (note the difference in integration limits). I know both integrals will give the same answer. But I
am confused bec

Consider the transformation w = (i - z) / (i + z).
The upper half plane Im z > 0 maps to the disk |w| < 1 and the boundary of the half plane maps to the boundary of the circle |w| = 1.
1. Show that a point z = x is mapped to the point
w = [(1 - x^2) / (1 + x^2)] + i[(2x) / (1 + x^2)],
and use this to find the i