Which of the following numbers is

not in the domain of the function
(f)=x(x^2-16)/x^2-5x-6

4 a
B) 4
C) 0
D) 6
E) 1

Expand the function:

x(x+4)(x-4)/(x+1)(x-6)

Your roots are -4,0,4 Therefore,

All real numbers except -1 and 6 are not in the domain of the function.

all reals except -1 and 6 are in the domain.

The answers have some typos.

To determine which of the numbers is not in the domain of the function, we need to identify any values of x that would make the denominator of the function equal to zero. That's because division by zero is undefined in mathematics.

The given function is f(x) = x(x^2-16) / (x^2-5x-6).

Let's examine the denominator, x^2-5x-6, and set it equal to zero:

x^2 - 5x - 6 = 0

To solve this quadratic equation, we can factor it:

(x-6)(x+1) = 0

From this equation, we can see that the denominator will be zero when x = 6 or x = -1.

Now, we can check which among 4, 0, 6, and 1 values are not in the domain of the function.

A) 4: This value is in the domain since it does not make the denominator zero.

B) 0: This value is also in the domain since it does not make the denominator zero.

C) 6: This value makes the denominator zero, so 6 is not in the domain of the function.

D) 1: This value is in the domain since it does not make the denominator zero.

Therefore, the number that is not in the domain of the function is 6, which is option (D).