## hby0214 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.

1. helder_edwin

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. helder_edwin

do u remember the definition of function?

3. hby0214

A function is a rule that assigns a unique element in Rn to Rm. It is one to one.

4. helder_edwin

the last part is something else.

5. helder_edwin

a function assigns a UNIQUE element to EVERY element of its domain.

6. hby0214

Ok I understand that.

7. hby0214

So a certain w and x cannot have two outputs.

8. helder_edwin

what does (w,x)=(1,-1) get assigned to?

9. helder_edwin

yes. precisely.

10. hby0214

(1,-1) is assigned to (1,1)?

11. helder_edwin

just that?

12. helder_edwin

let's see: $\large y=w=1$ right?

13. hby0214

right

14. helder_edwin

BUT $\large z^4=x^2=(-1)^2=1\Rightarrow z=\pm\sqrt[4]{1}=\pm1$

15. helder_edwin

so $\large (1,-1)\mapsto(1,1)$ and $\large (1,-1)\mapsto(1,-1)$

16. hby0214

So does that mean T is not a function?

17. helder_edwin

yes. that's what u were asked to prove.

18. hby0214

T is graph of something, but that something is not a function. right?

19. helder_edwin

yes.

20. hby0214

Thank you SO much!

21. helder_edwin

u r welcome.