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How to identify whether a function is implicit or explicit?

  1. Sep 5, 2010 #1
    how to identify whether a function is implicit or explicit?
    advanced thanks.
     
  2. jcsd
  3. Sep 5, 2010 #2

    hunt_mat

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    Re: implicit

    If a function is written (or can be written) as y=f(x) then it is explicit, if it only has the form f(x,y)=0 for example then it is implicit.
     
  4. Sep 6, 2010 #3
    Re: implicit

    suppose the equation is x^2/3 + y^2/3 = a^2/3. Is it a implicit function or explicit?
     
  5. Sep 6, 2010 #4

    hunt_mat

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    Re: implicit

    The equation can be written as:
    [tex]
    x^{\frac{2}{3}}+y^{\frac{2}{3}}-a^{\frac{2}{3}}=0
    [/tex]
    So according to my definition, it is implicit. The next question is is, can it be re-arranged to give y=f(x) for some f(x), this requires algebra to check and this is your job.
     
  6. Sep 7, 2010 #5
    Re: implicit

    but the function canbe written as y^2/3= a^2/3 - x^2/3.
    so it should be explicit. how implicit?
     
  7. Sep 7, 2010 #6

    hunt_mat

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    Re: implicit

    No, not just y^n, but y. If we take the roots then
    [tex]
    y=\pm (a^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}}
    [/tex]
    Why is this not a well defined function?
     
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