Question

What are the domain restrictions of the expression g^2+7g+12/g^2−2g−24 ?

Select each correct answer. ( pick more than 1)




g≠4

g≠6

g≠3

g≠−6

g≠−4

g≠−3

Answer 1

Explanation:

The domain restrictions of this expression stem from the denominator, g^2−2g−24. Remembering that we can NOT divide by zero, we purposely set g^2−2g−24 = 0 and solve for g; the resulting g values are the ones g cannot have here.

g^2−2g−24 = (g-6)(g+4) = 0. Then the forbidden g values are g = 6 and g = -4.

We can write the domain in set notation as: (-∞,-4) ∪ (-4,6) ∪ (6, infinity). Or

we can just type out the domain restrictions: g≠6 and g≠−4.

(-infinity, -4)∪

Answer 2

g ≠ -4 and g ≠ 6

Explanation:

Let,

`h(g)=(g^2+7g+12)/(g^2-2g-24)`

Which is a rational function,

Since, a rational function is defined for all real numbers except those for which denominator = 0,

If
`g^2 - 2g - 24=0`

By the middle term splitting,

`g^2 - (6g - 4g) - 24=0`

`g^2-6g+4g - 24=0`

`g(g-6)+4(g-6)=0`

`(g+4)(g-6)=0`

By the zero product property,

g + 4 = 0 or g - 6 = 0

⇒ g = -4 or g = 6

⇒ h(g) is defined for all real numbers except g = -4 and g = 6,

i.e. domain restriction is,

g ≠ -4 and g ≠ 6