Question

Determine the domain of the function

Answer 1

pick the numbers that would make the denominator \(x(x^2-16)=0\) and exclude those
does it help to know what \(x(x^2-16)=x(x-4)(x+4)\) ?

Answer 2

for any function that works for real numbers and provides real numbers as results we need to take care that any unreal values are not included. when the denominator becomes zero the function returns 1/0 = infinity which is not a real number.
so we have to exclude the values of x where the denominator becomes zero.
find x for
\[x(x^2-16) = 0\]

Answer 3

so either x = 0 or \[x^2-16=0\] which gives us \[x^2= 16\]\[x = +4 or -4\]
thus the function is valid for all real values of x except 0 +4 and-4. Did you understand?

Answer 4

I missed the x in the numerator, it would cancel out with the x in the denominator.
so x = 0 is not included in the answer.

Answer 5

so x ] x = 4

Answer 6

whats the domain

Answer 7

all numbers except -4, 0, 4

Answer 8

so is it a b c or d