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Thread: 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 = {$\displaystyle (x, y) \epsilon R X R | y = x^2 - 7x $}

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


    a) State the domain of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$
    b) State a defining equation of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$
    c) Why are the domains of $\displaystyle f \cdot g$ and $\displaystyle \frac {f}{g}$ 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 = {$\displaystyle (x, y) |x\in \mathbb{R}, y = x^2 - 7x $}

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

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

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

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

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