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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
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

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

hby0214Best 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_edwinBest ResponseYou've already chosen the best response.1
the last part is something else.
 one year ago

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

hby0214Best ResponseYou've already chosen the best response.0
So a certain w and x cannot have two outputs.
 one year ago

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

hby0214Best ResponseYou've already chosen the best response.0
(1,1) is assigned to (1,1)?
 one year ago

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

helder_edwinBest 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_edwinBest 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

hby0214Best ResponseYou've already chosen the best response.0
So does that mean T is not a function?
 one year ago

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

hby0214Best ResponseYou've already chosen the best response.0
T is graph of something, but that something is not a function. right?
 one year ago
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