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Math Help - Please help!

  1. #1
    Junior Member
    Joined
    Oct 2007
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    Smile Please help!

    Consider the function f(x) = Log(1/2)(x^2 - 2x + 3) and determine :


    ( A ) Its domain.
    ( B ) The intervals where it is strictly increasing.
    ( C ) The intervals where it is strictly decreasing.


    Thank you very much for your help!! I appreciate it!
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    x^2-2x+3>0, \ \forall x\in\mathbf{R}.
    So, the domain is \mathbf{R}.

    Let g(x)=\log_{\frac{1}{2}}x and h(x)=x^2-2x+3.
    Then f(x)=g(h(x))
    g(x) is decreasing for all x>0.
    h(x) is decreasing for all x\leq 1 and increasing for all x\geq 1.
    Then f is increasing for all x\leq 1 and decreasing for all x\geq 1.
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