Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
hby0214
Group Title
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.
 one year ago
 one year ago
hby0214 Group Title
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.
 one year ago
 one year ago

This Question is Closed

helder_edwin Group TitleBest ResponseYou've already chosen the best response.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 \(z^4=x^2\).
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
do u remember the definition of function?
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
A function is a rule that assigns a unique element in Rn to Rm. It is one to one.
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
the last part is something else.
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
a function assigns a UNIQUE element to EVERY element of its domain.
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
Ok I understand that.
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
So a certain w and x cannot have two outputs.
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
what does (w,x)=(1,1) get assigned to?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
yes. precisely.
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
(1,1) is assigned to (1,1)?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
just that?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
let's see: \[ \large y=w=1 \] right?
 one year ago

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

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
so \[ \large (1,1)\mapsto(1,1) \] and \[ \large (1,1)\mapsto(1,1) \]
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
So does that mean T is not a function?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
yes. that's what u were asked to prove.
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
T is graph of something, but that something is not a function. right?
 one year ago

hby0214 Group TitleBest ResponseYou've already chosen the best response.0
Thank you SO much!
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
u r welcome.
 one year ago
See more questions >>>
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.