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 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.
 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.

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

hby0214
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1the last part is something else.

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

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

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

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

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

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

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

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

hby0214
 2 years ago
Best ResponseYou've already chosen the best response.0T is graph of something, but that something is not a function. right?
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