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Math Help - Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

  1. #1
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    Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=



    This is from a a question i posted a while back but never got a good response to.

    "Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5]."


    now another question is find f|A composite XB (big with with subscript B)

    My teacher showed the graph for it. But i dont understand it.

    Could someone please help in how this graphs comes to be?? Thanks.
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  2. #2
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    So, we need to find f|_A\circ\chi_B where f|_A is the restriction of f to A and \chi_B is the characteristic function of B defined by

    \chi_B(x)=\begin{cases}1&x\in(2,5]\\0&\mbox{otherwise}\end{cases}

    Do you understand this definition of \chi_B(x)? This is a so-called piecewise-defined function. Can you find \chi_B(0), \chi_B(2), \chi_B(3), \chi_B(5), \chi_B(8)? What are all possible values of \chi_B(x)?
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    Yes i understand the definition. i understand the graph of XB. I dont understand what is meant by XB(0), XB(1).. and so forth though
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    I am genuinely curious about what you don't understand. First note that when I write

    \chi_B(x)=\begin{cases}1&x\in(2,5]\\0&\mbox{otherwise}\end{cases}

    \chi_B is being defined. The meaning of \chi_B is not composed of the meanings of \chi and B, as if you are supposed to know them already. No, one can replace \chi_B by some symbol f, and this would be a definition of a new function f(x).

    Could you explain how it is possible to understand the definition of a function and the graph of a function but not understand how to apply the function to a specific value? Do you understand the general concept of a function? Could you be more specific about what you do and do not understand?
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    I think its the whole concept of the characteristic function. it's only mentioned in a brief paragraph in our book. There really isn't any reasoning behind it. Our teacher didn't explain the purpose of what this is applied too, just decided give a question over it. So i don't know what to do when given this question. I hardly understand the notation. Thanks anyway guys .
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    The composition f|_A\circ\chi_B can be described by the following situation. Suppose you are a supervisor and you want to meet with your team. You decide do hold two meetings. You give each team member a paper slip with either 0 or 1 written on it. Then you tell everybody that if they get a slip with x written on it, they should come to the meeting at 2 - 3x pm. So, those with 1 come at 2 - 3(1) = -1 pm (let's agree that this is 11 am) and the rest come at 2 pm.

    Let B be the group that received 1. The function that for each person returns 0 or 1 is called the characteristic function of the group B; it sets apart people in B by saying that each person in that group received 1. The composition f|_A\circ\chi_B is analogous to a function that, given a person, returns the time of the meeting.
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    Re: Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=

    Another minor note: function composition (unfortunately) works in reverse. So you take a real number and plug it into the characteristic function for B before plugging the result into f. Since the range of B is {0, 1} and this lies in the domain of f|A, the function is defined everywhere on R. If A were instead, say, (0, 5], instead of taking value -1 in the range (2, 5] and 2 elsewhere, it would take value -1 in the range (2, 5] and be undefined elsewhere.
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