Find the domain of the function

[frctl]

The domain means the set of possible input values.

I am given the following function


Am I only concerned with the denominator and
if so, how do I factor out x² - x - 6?

 

[tkhunny]

You seem to be on the right track.

You are not "only concerned with the denominator", but that may be a reasonable thought process.

What values simply don't work in the definition? In this case, the good suspects are found by making the denominator zero (0).

 

[frctl]

x² -x - 6 = 0

Then I should use the quadratic formula

 

[Steven G]

How do you factor x^2 - x - 6?

You should use any of the methods you learned. Like completing the square, quadratic formula, ...

 

[frctl]

I don't know how to use the completing the square method with this equation.

 

[Steven G]

x² -x - 6 = 0

Then I should use the quadratic formula

x² -1x - 6 = 0. Can you think of two numbers which multiply out to -6 and add up to -1? If yes, then you put those two numbers next to x in (x )(x )

 

[frctl]

-3 and 2, then maybe (x - 3)(x + 2) = 0

 

[Steven G]

I don't know how to use the completing the square method with this equation.

Why not? What is different in this equation where you can't do it. Lets work on this.

x²-1x - 6 = (x² - 1x + ?) - 6 + ?. Fill in the ?.

 

[Steven G]

-3 and 2, then maybe (x - 3)(x + 2) = 0

I wouldn't know if that is correct or not? Do -3 and + 2 add up to -1 and multiply out to -6?? Can you multiply out (x-3)(x+2) and see if you get the correct results?

 

[frctl]

(x² - 1x + 3) - 6 + 2

I obtain
x² + 2x - 3x - 6
x² -x - 6

 

[Steven G]

(x² - 1x + 3) - 6 + 2

I obtain
x² + 2x - 3x - 6
x² -x - 6

I can only assume that you obtain x²+2x-3x-6 from (x²-1x+3) - 6 +2. First you added 3 and then added 2 which is not 0. How did you get +2 - 3x from (x²-1x+3) - 6 +2

Even if x² -x - 6 = (x² - 1x + 3) - 6 + 2 how does that help you find when x² -x - 6 = 0

 

[frctl]

You're right, I'm not sure now

(x-3)(x+2) = 0 is helpful

 

[tkhunny]

x² -x - 6 = 0

Then I should use the quadratic formula

You should use whatever means are at your disposal to solve the problem.
Don't question your methods so much that you experience paralysis.