A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 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.
anonymous
 3 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

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1well 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 \(z^4=x^2\).

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1do u remember the definition of function?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0A function is a rule that assigns a unique element in Rn to Rm. It is one to one.

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1the last part is something else.

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1a function assigns a UNIQUE element to EVERY element of its domain.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok I understand that.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So a certain w and x cannot have two outputs.

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1what does (w,x)=(1,1) get assigned to?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0(1,1) is assigned to (1,1)?

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1let's see: \[ \large y=w=1 \] right?

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1BUT \[ \large z^4=x^2=(1)^2=1\Rightarrow z=\pm\sqrt[4]{1}=\pm1 \]

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1so \[ \large (1,1)\mapsto(1,1) \] and \[ \large (1,1)\mapsto(1,1) \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So does that mean T is not a function?

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.1yes. that's what u were asked to prove.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0T is graph of something, but that something is not a function. right?
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.