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Maths question - range

  1. Jul 28, 2016 #1
    1. The problem statement, all variables and given/known data

    I was doing some multiple choice questions. One question was:

    "Which of the expressions below has the largest value for 0 < x < 1

    The two relevant options (dismissing those obviously wrong) were:

    x-1 (can't do superscript on my iPhone - that should read X to the power of -1 ie 1/x)

    Other option was x-1/2 meaning one over the square root of x

    I took the question to mean which equation gives the greatest range for values of x between zero and one.

    The answer was given as 1/x but that confuses me because a) both have the range from 1 < range < infinity It is true that for any individual x then 1/x is larger than one over the square root of x but I thought that you couldn't compare infinities in that way.

    Also I thought that if you take the square root of x then doesn't it have a positive and negative root such that you actually have a range of - infinity < range < -1 as well as the range 1 < range < infinity.

    Where am I going wrong?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 28, 2016 #2


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    You may have misinterpreted the question. What about this:

    For a given ##x## between ##0## and ##1##, which of the following expressions gives the largest value?

    On a second point about square roots. The square root of ##1## is ##1##. As in, ##\sqrt{1} = 1^{1/2} = 1## In other words, the square root has a unique, positive value.

    There is another "root", which is: ##y = -\sqrt{x}## which also has the property that ##y^2 = x##. But this ##y## is not the square root.
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