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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.
 2 years ago
 2 years 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.
 2 years ago
 2 years ago

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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 \(z^4=x^2\).
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
u r welcome.
 2 years ago
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