Question

what is the domain of the function $f(x) = \frac{2x^2 - 2x - 4}{x^2 + 2x - 24}$ ?
a. $x \
eq 6$ or $4$
b. $x \
eq -6$ or $-4$
c. $x \
eq 6$ or $-4$
d. $x \
eq -6$ or $4$

Explanation:

Step1: Set denominator to 0

$x^2 + 2x - 24 = 0$

Step2: Factor quadratic equation

$(x + 6)(x - 4) = 0$

Step3: Solve for x-values

$x + 6 = 0 \implies x = -6$; $x - 4 = 0 \implies x = 4$

Step4: Identify excluded x-values

Domain excludes $x = 6$ and $x = -4$, so $x
eq 6$ or $-4$

Answer:

C. $x
eq 6$ or $-4$