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    I'm struggling with this question:
    given that equation |f(x)|=k has two distinct roots, determine the possible values of k.

    f(x)=2-sqrt of x

    Thank you!
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    (Original post by Astana)
    I'm struggling with this question:
    given that equation |f(x)|=k has two distinct roots, determine the possible values of k.

    f(x)=2-sqrt of x

    Thank you!
    Best if you sketch |2- \sqrt{x}| then observe for which k the horizontal line y=k intersects it twice.
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    (Original post by RDKGames)
    Best if you sketch |2- \sqrt{x}| then observe for which k the horizontal line y=k intersects it twice.
    the answer is 0<k<2, but I'm really unsure how to get this
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    (Original post by Astana)
    the answer is 0<k<2, but I'm really unsure how to get this
    Well, have you made the sketch?
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    (Original post by RDKGames)
    Well, have you made the sketch?
    yes, but I still don't understand it. The intercept with the y-axis is at 2, and it cuts the x-axis at 4
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    Draw f(x) = 2 - root x.

    It's basically -root x + 2 so that's the transformations.

    Then |f(x)| would be just the negative part flipped over the y axis. Notice that now |f(x)|=k will have 2 solutions if k is between 0 and 2. Drawing any straight horizontal line here will have 2 solutions thefore 0<k<2.
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    (Original post by Astana)
    yes, but I still don't understand it. The intercept with the y-axis is at 2, and it cuts the x-axis at 4
    So then if you draw a straight horizontal line on the graph, where must it be for it to intersect your graph twice?
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    (Original post by RDKGames)
    So then if you draw a straight horizontal line on the graph, where must it be for it to intersect your graph twice?
    it can't intersect it twice because it's not a quadratic
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    (Original post by Astana)
    it can't intersect it twice because it's not a quadratic
    Not sure where you pulled this from as a reason.

    The red curve represents |2-\sqrt{x}| and the blue line represents y=k. These two will intersect twice when k takes which values...?

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    (Original post by RDKGames)
    Not sure where you pulled this from as a reason.

    The red curve represents |2-\sqrt{x}| and the blue line represents y=k. These two will intersect twice when k takes which values...?

    oh, I see, larger than 0 but equal or less than 2.

    Thank you
 
 
 
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