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Math Help - Express f(x) in terms of the Heaviside function

  1. #1
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    Express f(x) in terms of the Heaviside function

    This question is attached.

    Just in case you cannot see it, it asks to express the function f(x) in terms of the Heaviside function.

    f(x)=x+1 when x<-1
    3x when -1<x<1
    2-x when x>1

    I don't understand how to do this at all so please go easy on me. Baby steps .
    Attached Thumbnails Attached Thumbnails Express f(x) in terms of the Heaviside function-screen-shot-2011-10-19-12.06.jpg  
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  2. #2
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    Re: Express f(x) in terms of the Heaviside function

    Quote Originally Posted by softstyll View Post
    This question is attached.

    Just in case you cannot see it, it asks to express the function f(x) in terms of the Heaviside function.

    f(x)=x+1 when x<-1
    3x when -1<x<1
    2-x when x>1

    I don't understand how to do this at all so please go easy on me. Baby steps .
    It may help to look at f  '(x) . It is more directly related to the Heaviside function than is f(x).

    Do you know what the Heaviside function is?
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  3. #3
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    Re: Express f(x) in terms of the Heaviside function

    For x< -1, f(x)= x+ 1. For -1< x< 1, f(x)= 3x= x+ 1+ (3x- (x+1))= x+1+ (2x- 1). For x> 1, f(x)= 2- x= 3x+ (2- x- 3x)= 3x+ (2- 4x). How use those with H(x+1) and H(x-1).
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  4. #4
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    Re: Express f(x) in terms of the Heaviside function

    Quote Originally Posted by SammyS View Post
    It may help to look at f  '(x) . It is more directly related to the Heaviside function than is f(x).

    Do you know what the Heaviside function is?
    Yes I know the definition of the heaviside function
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  5. #5
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    Re: Express f(x) in terms of the Heaviside function

    Quote Originally Posted by HallsofIvy View Post
    For x< -1, f(x)= x+ 1. For -1< x< 1, f(x)= 3x= x+ 1+ (3x- (x+1))= x+1+ (2x- 1). For x> 1, f(x)= 2- x= 3x+ (2- x- 3x)= 3x+ (2- 4x). How use those with H(x+1) and H(x-1).
    How did you get those expressions for f(x)?
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  6. #6
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    Re: Express f(x) in terms of the Heaviside function

    Quote Originally Posted by softstyll View Post
    How did you get those expressions for f(x)?
    HoI merely used a bit of algebra.
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  7. #7
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    Re: Express f(x) in terms of the Heaviside function

    For example, if the problem had been
    f(x)= x^2 for x< 2 and f(x)= x^3- 3x for x\ge 2

    I would have thought "on the left (x< 2) I have x^2 so I have to have that without any H. For x> 2, I want x^2+ f(x)H(x)= x^2+ f(x)= x^3- 3x so f(x)= x^3- 3x- x^2, the formula wanted in the second interval with the formula from the first region subtracted off to cancel the x^2 that is no longer wanted.

    In other words, f(x)= x^2+ H(x-2)(x^3- 3x-x^2).
    Last edited by HallsofIvy; October 19th 2011 at 02:12 PM.
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