1. ## 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| )

2. ## Re: Domain and range

Domain can't include 2 or-2

3. ## Re: Domain and range

How did you get that?

4. ## Re: Domain and range

Originally Posted by tankertert
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| )

$\displaystyle |w| =\begin{cases}-w, & \text{if } w < 0 \\w, & \text{if } w \geq 0\end{cases}$

Hence :

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

Hence , domain is :

$\displaystyle w \in (-\infty , + \infty) \backslash \{-2,2 \}$

5. ## Re: Domain and range

Really need help guys.

how do i find range for first question and second?

6. ## Re: Domain and range

Originally Posted by tankertert
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 $\displaystyle f^{-1}$ is the range of f and vice-versa.

If we write $\displaystyle y= -2/(-3+ 9m)$ them $\displaystyle -3+ 9m= -2/y$ so $\displaystyle 9m= 3- 2/y$ and $\displaystyle m= 1/3 - 2/(9y)$. 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?