Question 1
Harmonic distortion is aserious problem for the electrical supply industry
and can cause overheating of induction motors and transformers and
cause the neutral conductor to carry more than its rated current

Harmonic distortion is caused by consumer loads requiring non-
sinusoidal currents. There are two main types of load that generate
harmonic cturents:

- Computers and other oﬁioe equiprnent. The typical wavdorm ofthe
current taken Irv such devices is shown in FIGURE 3{a}.
- Variable speed motor drives as used in the manufacturing indusry and in lifts. Typical current waveform of such loads is attached

See attached

The table below gives the complex Fourier coefficient obtained from
a 1oad's current waveform

{a} Use Ertoel's Fourier Analysis 'inverse' ﬁmction to transform the
complex coefficients back tothe original time domain values

{b} Use the time domain values to plot a graph ofthe wave form and
hence state if the waveform is from a TYPE A or a TYPE B load

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!

Define inverse function. Give a criterion for a function to have an inverse. Solve the following problems.
(1) Prove that the function f:R-->R, f(x)=3x+4 has an inverse, and find it.
(2) The function f:R-->R, f(x)=kx^2+3x+4 has an inverse. Find k.

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

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

1. What is an inverse function? In order for a function to have an inverse it must be a one-to-one function. Explain in your own words what it means to be a one-to-one function and why this is a necessary requirement for having an inverse. Give a simple example of a function and its inverse. Explain why these functions are in

Consider the following function f: R --> R defined by f(x) = x3 - 5 .
(a) Use the contrapositive to explain (no proof necessary) that f is a one-to-one function.
(b) Find f -1.
(c) Compute f o f.

Consider the function f(x) = arcsin(1 - x^2).
(a) What is the largest domain over which this function is defined?
(b) For this domain, what is the corresponding range of the function?
(c) If this function is one-to-one, find the inverse function f^-1(x), and state the domain of this inverse function. Otherwise, find a suitabl