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Math Help - questions on Characteristic functions

  1. #1
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    questions on Characteristic functions

    1) If f(x) = x^2, where x is an element of real nos, and X is the characteristic function of [0,9], of what subset of R is X.f the characteristic function?

    X is the the characteristic function of [0,9]. So
    X(x) =1 if x is in [0,9]
    X(x) =0 if x is not on [0,9]

    X.f = X(f(x)) = X(x^2)

    Now if B is a subset of R, whose characteristic function is X(x^2),
    then,
    X(x^2) = 1 if (x^2) is in B,
    X(x^2) = 0 if (x^2) is not in B.

    Then how do i proceed. I don't know. I think the answer is either [0,3] or [0,81]. but i am not able to work it out.

    2) Then immediately the successive question is :

    If f: A--> B and Xe is the char. fn. of E which is a subset of B. Of what subset of A is Xe.f the char. fn.?

    COuld you give me some hints on how to solve this one.
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  2. #2
    Senior Member Sampras's Avatar
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    Quote Originally Posted by poorna View Post
    1) If f(x) = x^2, where x is an element of real nos, and X is the characteristic function of [0,9], of what subset of R is X.f the characteristic function?

    X is the the characteristic function of [0,9]. So
    X(x) =1 if x is in [0,9]
    X(x) =0 if x is not on [0,9]

    X.f = X(f(x)) = X(x^2)

    Now if B is a subset of R, whose characteristic function is X(x^2),
    then,
    X(x^2) = 1 if (x^2) is in B,
    X(x^2) = 0 if (x^2) is not in B.

    Then how do i proceed. I don't know. I think the answer is either [0,3] or [0,81]. but i am not able to work it out.

    2) Then immediately the successive question is :

    If f: A--> B and Xe is the char. fn. of E which is a subset of B. Of what subset of A is Xe.f the char. fn.?

    COuld you give me some hints on how to solve this one.
    1. For  x \in [0,9] ,  x^2 \in [0,81] .
    Last edited by Sampras; June 26th 2009 at 09:03 PM.
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  3. #3
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    Ya so X.f is a characteristic function of [0,81]?
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