Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

hby0214

  • 2 years ago

Show that the set T ={(w,x,y,z)∈R4 such that y=w and x^2 =z^4} is not the graph of any function of w and x.

  • This Question is Closed
  1. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well u have the correspondence (i don't know if this is the word in english) \[ \large (w,x)\mapsto(y,z) \] such that \(y=w\) and \(z^4=x^2\).

  2. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do u remember the definition of function?

  3. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A function is a rule that assigns a unique element in Rn to Rm. It is one to one.

  4. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the last part is something else.

  5. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a function assigns a UNIQUE element to EVERY element of its domain.

  6. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I understand that.

  7. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So a certain w and x cannot have two outputs.

  8. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what does (w,x)=(1,-1) get assigned to?

  9. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. precisely.

  10. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (1,-1) is assigned to (1,1)?

  11. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    just that?

  12. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let's see: \[ \large y=w=1 \] right?

  13. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  14. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    BUT \[ \large z^4=x^2=(-1)^2=1\Rightarrow z=\pm\sqrt[4]{1}=\pm1 \]

  15. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so \[ \large (1,-1)\mapsto(1,1) \] and \[ \large (1,-1)\mapsto(1,-1) \]

  16. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So does that mean T is not a function?

  17. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. that's what u were asked to prove.

  18. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    T is graph of something, but that something is not a function. right?

  19. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes.

  20. hby0214
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you SO much!

  21. helder_edwin
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    u r welcome.

  22. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.