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Math Help - g(x,y)=f(x,y) for all (x,y)

  1. #1
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    g(x,y)=f(x,y) for all (x,y)

    f(x,y)=(x)/ (1-y2), y does not equal 1 or -1

    Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.


    I really don't know where to begin...
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  2. #2
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    Quote Originally Posted by genlovesmusic09 View Post
    f(x,y)=(x)/ (1-y2), y does not equal 1 or -1

    Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.


    I really don't know where to begin...
    Thinking about this more I was wondering if possibly g(x,y)= x/1+y^2

    because that function is defined and continuous...
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  3. #3
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    Quote Originally Posted by genlovesmusic09 View Post
    Thinking about this more I was wondering if possibly g(x,y)= x/1+y^2

    because that function is defined and continuous...

    Indeed, but g(x,y)\neq f(x,y)...for example, g(1,2)=\frac{1}{5}\neq -\frac{1}{3}=f(1,2)

    The problem has no solution since f cannot be redefined (which in fact is what you want) in \pm 1 as \lim_{(x,y)\to (x_0,\pm 1)}f(x,y) doesn't exist.

    Tonio
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