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Functions of Several Variables

  1. Feb 12, 2009 #1
    My question is mostly down to staggering ignorance of basic notation. I have been unable to find a straightforward answer anywhere - so I assume it must be pretty basic.

    I have a function: [tex]f(x,y)=x^3+y^3-3x-12y+20[/tex]

    Given that I know a value of x, ie [tex]x=-1[/tex], how do I extract a value of y using this notation?

    I know when [tex]f(x)=x^2[/tex] I can use substitute [tex]f(x)[/tex] with [tex]y[/tex], but I find myself stuck with what to substitute [tex]f(x,y)[/tex] with...
  2. jcsd
  3. Feb 12, 2009 #2


    Staff: Mentor

    In order to evaluate your f(x, y), you need two numbers. What you get out isn't a y value; it's a z value. To graph the function, you need three dimensions. If you know a z value and an x value, there's the possibility that you can solve for the value you don't know: y. For example, if you know that f(x, y) = 10 and that x = 1, you might be able to solve the equation 10 = 1^3 + y^3 -3(1) - 12y + 20 to get y.

    Does that make sense?
  4. Feb 12, 2009 #3
    Yes, it actually does. Thank you Mark.
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