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Math Help - Domain and range

  1. #1
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    Domain and range

    Hi.

    Two questions.

    1: f(m) = -2 / (-3+9m)

    i got a domain (-infinity, 0.33) U (0.33, infinity) and range (-infinity, 0) U (0, inifinity). correct?

    2: f(w) = 7 / ( -2 + |w| )

    i have no idea about number two. help please~!
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  2. #2
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    Re: Domain and range

    Domain can't include 2 or-2
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  3. #3
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    Re: Domain and range

    How did you get that?
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  4. #4
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    Re: Domain and range

    Quote Originally Posted by tankertert View Post
    Hi.

    Two questions.

    1: f(m) = -2 / (-3+9m)

    i got a domain (-infinity, 0.33) U (0.33, infinity) and range (-infinity, 0) U (0, inifinity). correct?

    2: f(w) = 7 / ( -2 + |w| )

    i have no idea about number two. help please~!
    |w| =\begin{cases}-w, & \text{if } w < 0 \\w, & \text{if } w \geq 0\end{cases}

    Hence :

    f(w) =\begin{cases}\frac{-7}{w+2}, & \text{if } w < 0 \\\frac{7}{w-2}, & \text{if } w \geq 0\end{cases}

    Hence , domain is :

    w \in (-\infty , + \infty) \backslash \{-2,2 \}
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  5. #5
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    Re: Domain and range

    Really need help guys.

    how do i find range for first question and second?
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  6. #6
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    Re: Domain and range

    Quote Originally Posted by tankertert View Post
    Hi.

    Two questions.

    1: f(m) = -2 / (-3+9m)

    i got a domain (-infinity, 0.33) U (0.33, infinity)
    Well, it would be far better to write "domain (-infinity, 1/3) U (1/3, infinity)". Do you see why?

    and range (-infinity, 0) U (0, inifinity). correct?
    One way to handle a "range" problem is to convert it into a "domain" problem by looking at the inverse function. The domain of f^{-1} is the range of f and vice-versa.

    If we write y= -2/(-3+ 9m) them -3+ 9m= -2/y so 9m= 3- 2/y and m= 1/3 - 2/(9y). Now what value can y not be?


    2: f(w) = 7 / ( -2 + |w| )
    Much the same. We cannot have -2+ |w|= 0 so we cannot have |w|= 2. What values of w are forbidden?
    (This is the one biffboy was referring to.)

    As for the range, again, let y= 7/(-2+ |w|) so that |w|- 2= 7/y so |w|= 2+ 7/y. What can y not be?

    i have no idea about number two. help please~![/QUOTE]
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