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Math Help - Product and Quotient of Functions

  1. #1
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    Product and Quotient of Functions

    I don't know how to start this problem...because I don't understand the given sets...

    Given:

    f = { (x, y) \epsilon R X R | y = x^2 - 7x }

    g = { (x, y) \epsilon R X R | y = x}


    a) State the domain of f \cdot g and \frac {f}{g}
    b) State a defining equation of f \cdot g and \frac {f}{g}
    c) Why are the domains of f \cdot g and \frac {f}{g} different?
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  2. #2
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    Quote Originally Posted by Macleef View Post
    I don't know how to start this problem...because I don't understand the given sets...

    Given:

    f = { (x, y)  |x\in \mathbb{R}, y = x^2 - 7x }

    g = { (x, y) | x\in \mathbb{R}, y = x}
    a) State the domain of f \cdot g and \frac {f}{g}

    The domain of f\cdot g is the intersection of the domain of f and g which is still \mathbb{R}

    The domain of f/g is the intersection of the domain of f and g and g\not = 0 thus it is \mathbb{R} \setminus \{ 0 \}
    b) State a defining equation of f \cdot g and \frac {f}{g}
    f\cdot g = \{ (x,y)|x\in \mathbb{R}, y = x(x^2-7x)\}
    f/g = \{(x,y)| x\in \mathbb{R} \setminus \{ 0 \}, y = (x^2-7x)/x=x-7\}
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    The domain of f\cdot g is the intersection of the domain of f and g which is still \mathbb{R}

    The domain of f/g is the intersection of the domain of f and g and g\not = 0 thus it is \mathbb{R} \setminus \{ 0 \}

    f\cdot g = \{ (x,y)|x\in \mathbb{R}, y = x(x^2-7x)\}
    f/g = \{(x,y)| x\in \mathbb{R} \setminus \{ 0 \}, y = (x^2-7x)/x=x-7\}
    For a, do you mean the domain is { x^2 - 7x, 7x} for f  \cdot g?
    and for \frac {f}{g}, the domain is what?
    Last edited by Macleef; January 7th 2008 at 05:15 PM.
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