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Math Help - a question about finding the number of Implicit Functions in an equation

  1. #1
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    a question about finding the number of Implicit Functions in an equation

    hi evreyone,
    guys how can i solve a question like this:
    How many implicit functions are determined by the equation:

    x^4 + y^4 - 1 = 0
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  2. #2
    TD!
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    Because of the even power (i.c. 4), it breaks down to minimally two functions.
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  3. #3
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    thanks TD for the reply i don't know but my answear before i look into the solution was the same as yours but in the book called Calculus for Swokoski it says an infinite number. so if anyone can explain the answear to me i would be gratefull.
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  4. #4
    TD!
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    Well I said minimally; i.e. you can't express it in a smaller number of functions.
    Of course, trivially, you can always break it up into (infinitely many) different functions.
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  5. #5
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    how can i break it into infinitaley other functions?you mean i will be expressing x as another function of time for example?and how can a numebr after being square rooted be negative?
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  6. #6
    TD!
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    You can define the two function I gave, piecewise.

    The square root of a real number is positive, but x = 9 has solutions x = +sqrt(9) and x = -sqrt(9) with sqrt(9) being 3, so x is either 3 or -3.
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