Pairing the domain or range of the function correctly

[dom1]

I know how to solve the domain of that function, like a problem- f(x)=sqrt x^2-9,

I know how to get 3, but the correct answer is (-infinity, -3], [3,+infinity). Im confused

on how to put it in that certain pairing. Thank you.

 

[xomandi]

i am also confused to that..

the () or "closed parenthesis" mean that the function goes as close as it can to the number (after,before) but it doesnt TOUCH that number, while the open bracket means that it CAN touch that number.

in that problem, you should not be able to include 3 or -3 since it would make the denominator 0, which is not allowed

 

[stapel]

I'm sorry, but I don't understand your question. You say you know how to find the domain of a function such as f(x) = sqrt[x² - 9], but then say that you don't understand how to find the domain for f(x) = sqrt[x² - 9]...?

Please clarify. Thank you.

Eliz.

 

[dom1]

I know how to get 3, like x^2-9=0+9, then X^2=9, then I get 3 from squaring the 9 from x, but i'm confused on how they paired it into 2 answers (-infinity, 3], [3,+infinity).

 

[xomandi]

its from - infinity to -3 because when you square -3 it is also positive 9

 

[stapel]

I know how to get 3, like x^2-9=0+9, then X^2=9, then I get 3 from squaring the 9 from x, but i'm confused on how they paired it into 2 answers (-infinity, 3], [3,+infinity).

So you don't actually understand how to find domains then. (Solving for x-intercepts is not the same as finding domains.)

The "domain" of a function is all allowable x-values. To find the domain of a function, the usual process is to find any problem values, and then set the domain as "everything else".

For instance, for y = 1/(x + 2), the function will be undefined if the denominator is zero. So you would solve x + 2 = 0, and determine that the old problem is at x = -2. Then the domain is "all x not equal to -2".

Or if y = sqrt[3 - x], then the function will be undefined if there is a negative inside the radical. So you would solve for the values that aren't a problem: 3 - x > 0 means x < 3. So that's the domain.

In your case, you would be solving "x² - 9 > 0". Do you know anything about solving quadratic inequalities? Or would you be needing a link to a lesson on that topic as well?

Thank you.

Eliz.