Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?

A 4x + 8

B 2x + 12

C x2 - 4

D x2 - 16

x² - 4 would be the denominator in Sally's function ⇒ answer (C)

Step-by-step explanation:

* In any rational function the domain of it (values of x) is all the

real numbers except the numbers which make the

denominator = 0

* Ex: In x - 3/x - 2

∵ The denominator = x - 2

∵ The value of x which make the denominator = 0 is 2

∴ The domain is all real number except 2

* So If you want to know the denominator search for the

values which make the denominator equal to zero.

* In the problem sally found that a solution of x = 2 was

extraneous for the function

- That means the function not defined at x = 2

∵ x = 2⇒ subtract 2 from both sides

∴ x - 2 = 0

* Now look to the answer and find which one when you

equate it by 0 give you the answer x = 2

A) ∵ 4x + 8 = 0 ⇒ subtract 8 from both sides

∴ 4x = - 8 ⇒ : 4

∴ x = - 2 ⇒ not the answer

B) ∵ 2x + 12 = 0 ⇒ subtract 12 from both sides

∴ 2x = - 12 ⇒ : 2

∴ x = - 6 ⇒ not the answer

C) ∵ x² - 4 = 0 ⇒ add 4 to the both sides

∴ x² = 4 ⇒ take √ to both sides

∴ x = ± 2 ⇒ the answer

* That means x = 2 or x = - 2

* x² - 4 would be the denominator in Sally's function