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Math Help - Solve f(x) = 0

  1. #1
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    Solve f(x) = 0

    I have a Piecewise function, that looks like,

    -x , for x < - 1
    4- X^2 , for -1 < X < 2
    SQRT X-2 -1 , 2 < X < 11

    Solve f (x) = 0


    I am having troubles find where to start.
    Do I want to plug in and solve = 0 to each equation?
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  2. #2
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    Re: Solve f(x) = 0

    try sketching the piece-wise function first ...


    btw, this problem should be in the precalculus forum ... it's not advanced algebra.
    Last edited by skeeter; October 16th 2012 at 02:23 PM.
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  3. #3
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    Re: Solve f(x) = 0

    Quote Originally Posted by wolfwood View Post
    Do I want to plug in and solve = 0 to each equation?
    That's certainly one way to do it - although you'd then need to check that any x value you found that makes f zero is in that part of the domain.

    To get you started:
    Does f(x) = 0 have a solution on the interval x<-1? (That's the interval (-\infty, -1).)
    Solve f(x)=0 on the interval x<-1.
    So solve -x=0 on the interval x<-1.
    That equation has one solution, x=0, but x=0 isn't in that interval (x<-1, the interval (-\infty, -1) ).
    Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval (-\infty, -1) ).
    Last edited by johnsomeone; October 16th 2012 at 02:25 PM.
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  4. #4
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    Lightbulb Re: Solve f(x) = 0


    Update: Exclusions removed
    Attached Thumbnails Attached Thumbnails Solve f(x) = 0-f-x-0.png  
    Last edited by MaxJasper; October 16th 2012 at 03:00 PM.
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  5. #5
    Behold, the power of SARDINES!
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    Re: Solve f(x) = 0

    Quote Originally Posted by MaxJasper View Post
    Careful there with the or equal to part of the inequality



    You forgot the "holes" in the graph. Note that one of them is at x=2, so it cannot be a zero!
    Attached Thumbnails Attached Thumbnails Solve f(x) = 0-graph.jpg  
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  6. #6
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    Re: Solve f(x) = 0

    Quote Originally Posted by johnsomeone View Post
    That's certainly one way to do it - although you'd then need to check that any x value you found that makes f zero is in that part of the domain.

    To get you started:
    Does f(x) = 0 have a solution on the interval x<-1? (That's the interval (-\infty, -1).)
    Solve f(x)=0 on the interval x<-1.
    So solve -x=0 on the interval x<-1.
    That equation has one solution, x=0, but x=0 isn't in that interval (x<-1, the interval (-\infty, -1) ).
    Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval (-\infty, -1) ).
    So for the next equation I got X = -2, or X = 2. X can not equal -2 since it is not agree with the interval, but X can equal 2. Am I getting the right idea?
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  7. #7
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    Re: Solve f(x) = 0

    Does it mean x=2 is not a root?

    Update: thanks, exclusions removed.
    Last edited by MaxJasper; October 16th 2012 at 03:00 PM.
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  8. #8
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    Re: Solve f(x) = 0

    Quote Originally Posted by MaxJasper View Post
    Does it mean x=2 is not a root?

    Update: thanks, exclusions removed.
    x = 2 is not in the function's domain
    Thanks from wolfwood
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  9. #9
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    Re: Solve f(x) = 0

    It was X = Sqrt(4), but i simplified it to X = 2 or x = -2
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  10. #10
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    Re: Solve f(x) = 0

    Quote Originally Posted by wolfwood View Post
    So for the next equation I got X = -2, or X = 2. X can not equal -2 since it is not agree with the interval, but X can equal 2. Am I getting the right idea?
    Yes, that's the right idea, but I think you overlooked something here (as MaxJasper and skeeter pointed out).
    The problem says f(x) = 4-x^2 when -1 < x < 2, but x=2 is not in that interval.
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  11. #11
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    Re: Solve f(x) = 0

    Oh yeah your right.
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