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

Please help with the following problems regarding limits and piecewise functions.
1) Let f(x) {o if x is a natural odd number
{1 otherwise
Does f(x) have a limit as x approaches infinity? Explain you answer.
2) Let f(x) {1 if x is a natural odd number
{ 1-1/x

Hello,
I was hoping someone could help me with this homework problem? I have looked through my text and notes and I cannot figure this out.
The problem is below.
Thank you, in advance, for your help!!
Prove the following: If x is any odd integer and y is any odd integer then xy is an odd integer.

Signal Processing & Wavelength. Problems # 6-7. See attached file for full problem description.
6. For each of the signals given, determine mathematically if the signal is even, odd, or neither. Sketch the waveforms to verify your results. For signals that are neither, find the even or odd parts of the signal.
a) x(t) = 5u(t

How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function? How would you change your explanation for someone who had taken high school algebra?

An even function is defined as f(x) = f(-x), and an odd function has -f(x) = f(-x).
The domain of a function is the set of input data that keeps the function defined.
Determine if the function f(x) = -2x^2 * absolute value(-6x) is even, odd, or neither.
Find the average rate of change for the function f(x) = 4/(x+3) between t

Please show as much working as possible and comment where possible.
Compare the values of f(x) and f(-x) to show which of the following are odd, even or neither. Give a reason for each.
Please see the attachment for complete question.

Please see the attached file for the fully formatted problems.
Let V be a vector space of all real continuous function on closed interval [ -1, 1]. Let Wo be a set of all oddfunctions in V and let We be a set of all evenfunctions in V.
(i) Show that Wo and We are subspaces and then show that V=Wo⊕We.
(ii) Find a pro