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Level Sets

  1. Oct 21, 2006 #1
    I'm having a really hard time with this question....

    Consider the function g: [0,infinity) --> R shown in figure 7 (Figure 7 is just a graph of a curve defined as z=g(s), where the horizontal axis is the s-axis) Let f be a new function given by: z = f(x,t) = g((x^2)+(t^2)-1). Plot the level set: f(x,t)=2. Classify the surface f.

    My problem is that it doesn't give me an equation to stick the input into, just some graph ....help!
  2. jcsd
  3. Oct 21, 2006 #2


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    Staff Emeritus
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    And I don't even have the graph!
    [tex]f(x,y)= g(x^2)+ y^2- 1= 2[/tex]
    [tex]g(x^2)+ y^2= 3[/tex]
    If g is linear (if the graph is a straight line), with positive slope, then this is an ellipse; with negative slope, a hyperbola. Whatever g is, we can see that the surface will be symmetric in both x and y. Without having some idea of what the graph of g looks like, I don't think we can say more.
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