Answer:
Choice c.
Step-by-step explanation:
The domain of a rational function is found where the denominator of the fraction is equal to 0. These are the values that are NOT allowed. We have to factor the denominator completely to find these values that make the denominator equal 0. In other words, our denominator right now is:
[tex]x(x^2-16)[/tex]
we set each factor equal to 0:
x = 0 or
[tex]x^2-16=0[/tex]
The left side of that quadratic is the difference of perfect squares, so it factors into the 2 binomials:
(x + 4)(x - 4)
Setting each of those equal to 0 we can solve for the values of x that are not allowed:
If x + 4 = 0, then
x ≠ 4.
If x - 4 = 0, then
x ≠ -4
So the domain for this rational function is:
{x I x ≠ ±4, x ≠ 0},
which is c.
