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Math Help - Domain of a function

  1. #1
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    Domain of a function

    f(x,y) = Sqrt(y-x^2)/(x^2+(y-1)^2) Find and graph the domain of the function
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  2. #2
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    Quote Originally Posted by Link88 View Post
    f(x,y) = Sqrt(y-x^2)/(x^2+(y-1)^2) Find and graph the domain of the function
    The domain of \sqrt{x} is all x\ge 0 so you must have y- x^2\ge 0. Graph y= x^2. y\ge x^2 for all (x,y) below that graph. The domain of 1/x is all x not equal to 0. The domain of \frac{1}{x^2+(y-2)^2} is all (x, y) except the single point where that denominator is 0. The domain of f is the points that are in both of those domains.
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  3. #3
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    Hello, Link88!

    Find and graph the domain of: . f(x,y) \;=\; \sqrt{\frac{y-x^2}{x^2+(y-1)^2}}

    The radicand must be positive.

    The denominator is always positive except at (0,1) where the function is undefined.

    The numerator must be nonnegative: . y - x^2 \:\geq \:0 \quad\Rightarrow\quad y \:\geq \:x^2
    . . This is the set of points on and above the parabola: y \,=\,x^2

    The region looks like this:
    Code:
         :::::::::::|:::::::::::
         *::::::::::|::::::::::*
          ::::::::::|::::::::::
          *:::::::::|:::::::::*
           *::::::::o::::::::*
             *::::::|::::::*
                *:::|:::*
        - - - - - - * - - - - - -
                    |
    where there is a "hole" at (0,1).

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