Answer:
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
* <em>Ex:</em> 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
