Question

What are the domain restrictions of the expression g^2−2g−24/g^3−4g^2−12g?

Select each correct answer.


Responses

g≠6
g ≠ -6
g≠−4
g≠0
g≠−2
g≠2

Answer 1

When working with rational functions, your main concern to not divide by 0. Dividing by 0 can't be done.

So, you need to look at the denominator of your fraction and figure out what values of g will make that denominator become 0.

Option #1 is to plug in each option from your list to see which ones make the denominator equal 0. If that g-value makes the denominator equal zero, then it has be excluded.

Option #2 is to set the denominator equal to 0 and solve that equation:
g^3 - 4g^2 - 12g = 0

To solve this, you could do it by factoring.

g^3 - 4g^2 - 12g = 0

g ( g^2 - 4g -12) = 0

g ( g - 6 ) ( g + 2) = 0

This splits into:
g = 0, g = 6, g = -2

So those are the three values of g that you cannot use.

g ≠ 0; g ≠ 6, g ≠ –2