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Homework Help: Function proof and range

  1. Sep 27, 2011 #1
    Let F: [-2,5] --> R be function with rule F(x) = x^2 - 1. Show range of F = [-1,24].

    I get that 5^2 = 25 - 1 = 24, but how does one get the lower bound of the range to be -1?
  2. jcsd
  3. Sep 27, 2011 #2


    Staff: Mentor

    52 [itex]\neq[/itex] 24, but F(5) = 52 - 1 = 24.

    Sketch a graph of the function and you should be able to see why the minimum value in the range is -1.
  4. Sep 27, 2011 #3
    Understood but unfortunately I can't use the graph to show it. They want us to use the definition of set equality and range of a function to do it.

    I understand that for two sets to be equal, A must be a subset of B and B must be a subset of A. For range of a function f from A to be, y is an element of B such for all x in A, x,y must both be elements of F. But I'm not making the connection between the two definitions and the question.
  5. Sep 27, 2011 #4
    To test for maxima and minima, you look at the two points onthe end of the interval (-2 and 5 in this case), then look at where F'(x) = 0.
  6. Sep 27, 2011 #5


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    How do you find the minimum of a function?
  7. Sep 27, 2011 #6


    Staff: Mentor

    Just because you can't use a graph to show what you need to show, that's not a good reason to skip that step. A graph might help you understand the function you're working with. Your function describes a portion of a very simple geometric figure. It's not clear to me that you realize this.
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