SS__
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Need some help on this:

Function f : (x, y) -> (xy, x^3)
Describe f^3 =: f . f . f

Any help is appreciated
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RDKGames
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(Original post by SS__)
Need some help on this:

Function f : (x, y) -> (xy, x^3)
Describe f^3 =: f . f . f

Any help is appreciated
f(x,y) = (xy,x^3)

ff(x,y) = f(xy,x^3) = (?,?)

fff(x,y) = f(?,?) = (??,??)
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NotNotBatman
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 x \mapsto xy i.e. first coordinate maps to (1st coordinate  \times 2nd coordinate)
y \mapsto x^3

xy is now our new "x" and the rule is f maps "x" to "xy" i.e. (1st coordinate  \times 2nd coordinate) as above

so under f again (xy) \mapsto xy \times x^3 which is (new x) \times (new y)
get it?
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SS__
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(Original post by RDKGames)
f(x,y) = (xy,x^3)

ff(x,y) = f(xy,x^3) = (?,?)

fff(x,y) = f(?,?) = (??,??)
Not sure what's happening in that second step?
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joshmaxyer
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the nswer is 47328653465749754169732065703465148735637856476547567430657.1
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RDKGames
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(Original post by SS__)
Not sure what's happening in that second step?
ff(x,y) = f(\underbrace{f(x,y)}_{=(xy,x^3)}) = f(xy,x^3)
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SS__
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(Original post by RDKGames)
ff(x,y) = f(\underbrace{f(x,y)}_{=(xy,x^3)}) = f(xy,x^3)
What would f(xy, x^3) be? Is it ((x^4)y, x^3y^3)?
Last edited by SS__; 1 year ago
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ghostwalker
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(Original post by SS__)
What would f(xy, x^3) be? Is it ((x^4)y, x^3y^3)?
Yes.
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SS__
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(Original post by ghostwalker)
Yes.
I got (x^7y^4,x^9y^9) for fff(x,y). How do I use these to describe the function?
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ghostwalker
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(Original post by SS__)
I got (x^7y^4,x^9y^9) for fff(x,y). How do I use these to describe the function?
First component is correct, second one isn't - you cubed the wrong part.

Other than stating what the function fff is in terms of the coordinates, I don't think there's anything you can say.
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SS__
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(Original post by ghostwalker)
First component is correct, second one isn't - you cubed the wrong part.

Other than stating what the function fff is in terms of the coordinates, I don't think there's anything you can say.
Oh, would it be x^12y^3 instead? And the question just says describe function f^3 so I guess that's all I can do
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ghostwalker
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(Original post by SS__)
Oh, would it be x^12y^3 instead?
For the second component, yes.
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RDKGames
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(Original post by SS__)
Oh, would it be x^12y^3 instead? And the question just says describe function f^3 so I guess that's all I can do
f^3(x,y) = (X,Y) is one way to describe it, otherwise you can stick with their notation and say

f^3 : (x,y) \mapsto (X,Y)
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