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Math Help - Range and Domain of Functions

  1. #1
    Junior Member cupid's Avatar
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    Range and Domain of Functions

    Find the Domain of


    I can do this Question using graphs. I need help in doing it without graphs ... some help please


    Find the Domain of


    -1 <= [2x^2 - 3] <= 1

    -1 <= (2x^2 - 3) < 2

    1 <= x^2 < \frac{5}{2}

    Why?
    |x| >= 1 and |x| < \sqrt{\frac{5}{2}}

    x \in (-\sqrt{\frac{5}{2}},-1]\cup[1,\sqrt{\frac{5}{2}})

    but the answer is

    x \in [-\sqrt{\frac{5}{2}},-1]\cup[1,\sqrt{\frac{5}{2}}]

    Why is the 5/2 terms included?
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  2. #2
    Junior Member cupid's Avatar
    Joined
    Feb 2011
    Posts
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    never mind about the second one ... its probably editor's carelessness

    But i really need help with the first one

    I've got this so far:

    |sin^{-1}sin x| \geq cos^{-1}cos x

    |sin^{-1}sin x| \ = \ sin^{-1}sin x, \ when \ sin^{-1}sin x \geq 0 \implies sin x\geq0 \implies x \in [0,\pi] \ in \ [0,2\pi]

    = \ -sin^{-1}sin x \ when \ sin^{-1}sin x \leq 0 \implies sin x \leq 0 \implies x \in [\pi,2\pi] \ in \ [0,2\pi]

    so

    sin^{-1}sin x \geq cos^{-1}cos x \ \forall \ x \in [0,\pi]

    -sin^{-1}sin x \geq cos^{-1}cos x \ \forall \ x \in [\pi,2\pi]

    Now what ???

    Please Reply ... i have nothing new to post now ... and the moderator will kill me if i again dump in a thread
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