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Math Help - A freaky function of circle

  1. #1
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    A freaky function of circle

    Hi everyone.
    So i have the curve (x^2 - 1)^2 + (y^2 - 1)^2 = 1

    My question is: Why can "y" not be written as a function of x? I need to shall this somehow.
    Thx for any help.
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by Snowboarder View Post
    Hi everyone.
    So i have the curve (x^2 - 1)^2 + (y^2 - 1)^2 = 1

    My question is: Why can "y" not be written as a function of x? I need to shall this somehow.
    Thx for any help.
    A function must have only one output for a given input, but in this equation there is more than one value of y per value of x.

    for example this equation is satisfied for the points (1,\sqrt{2}) and (1,-\sqrt{2}) and (1,0)

    That is three different values of y which satisfy this equation for a single value of x. Thus y cannot be a function of x.
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