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Math Help - Functions - Set of Values

  1. #1
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    Wink Functions - Set of Values

    1. Let f(x)=$\sqrt{(1/x^2)-2)}$

    Find

    a) The set of real values of x for which f is real and finite

    b) The range of f

    2.

    Let f(x)=(x+4)/(x+1) , x ≠ -1 and g(x)=(x-2)/(x-4) x ≠ 4

    Find the set of values of x such that f(x) ≤ g(x)

    Please help. Thanks!
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    Hi

    f(x)=$\sqrt{(1/x^2)-2)}$

    f is defined when (1/x^2)-2 \geq 0


    Let f(x)=(x+4)/(x+1) , x ≠ -1 and g(x)=(x-2)/(x-4) x ≠ 4

    g(x) \geq f(x)

    \displaystyle \frac{x-2}{x-4} - \frac{x+4}{x+1} \geq 0

    Use the same denominator to simplify this expression
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