## qwerties 2 years ago Apologize for troll, but I have one question...

1. qwerties

Once I plot y = x^y, I notice that it does not pass vertical line, hence not function. i dont understand one thing... it can be rewrite as y = x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x... why is it not function?

2. qwerties

y = x is function, y = x^x is function, y = x^x^x is function too and so on. why isnt y=x^y function?

3. etemplin

i think because to re-write that, you plug the function into itself, which doesnt work

4. lgbasallote

whoever said y = x^y isn't a function?

5. qwerties

Well, it doesnt follow the pattern (see my second reply) if the number of exponent is finite, it is function, otherwise its not. why?

6. qwerties

@lgbasallote plot it yourself and you can notice it doesnt pass vertical line test

7. lgbasallote

if you try to solve for x y = ylnx y/y = lnx 1 = lnx can you now see why it's not a function?

8. qwerties

should have thought of that. thanks

9. hartnn

what the ... ?

10. lgbasallote

but seriously...who said it isn't a function?

11. hartnn

ln y = ylnx

12. lgbasallote

and...what did i just do?

13. qwerties

@lgbasallote well, it isnt, right?

14. qwerties

you just proved this.

15. lgbasallote

@hartnn exactly..that's why i'm wondering why qwerties is saying it isn't a function

16. qwerties

wait...

17. lgbasallote

@qwerties i manipulated my algebra to make it look like not a function

18. lgbasallote

but if you look carefully there is a fallacy in my solution

19. qwerties

well, it doesnt pass vertical test. can you explain it?

20. qwerties

if it doesnt pass vertical line test, is it mean it still can be function?

21. lgbasallote

y = x^y according to my math vocabulary is what others call a recursive "function"