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Range of Values

This topic has 1 expert reply and 0 member replies
krishna kumar Junior | Next Rank: 30 Posts Default Avatar
Joined
11 Jun 2010
Posted:
15 messages

Range of Values

Post Fri Jun 25, 2010 5:36 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Hi,

    This one stumped me.

    If x^2 - 2 < 0, which of the following specifies all the possible values of x ?

    A. 0 < x < 2
    B. 0 < x < root(2)
    C. -root(2) < x < root(2)
    D. -2 < x < 0
    E. -2 < x < 2

    The OA is C

    I've come to the point where x < root(2) and x < -root(2).

    Thanks

    krishna kumar

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    Post Fri Jun 25, 2010 5:40 am
    Hey Krishna,

    You're very close. It's actually:

    x < root(2) and x > -root(2).

    When you have a variable raised to an even exponent, and the expression (in this case x^2) is less than a certain value, the resulting range is always a single bounded region.

    You can rewrite the expression in the prompt as x^2 < 2. The resulting breakdown is x > -root(2) and x < root(2). That in turn can be written as a single bounded region: -root(2) < x < root(2)

    If the problem instead specified x^2 > 2, then the result would be two unbounded regions, namely:

    x < -root(2) and x > root(2)

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