Answer:
Option B is correct.
The domain of the function h(x) is: [tex]\{x | x\neq \pm 6 , x\neq 0\}[/tex]
Step-by-step explanation:
Domain states that the complete set of all the possible values of the independent variable where function is defined.
Given the function:
[tex]h(x) = \frac{9x}{x(x^2-36)}[/tex]
To find the excluded value in the domain of the function.
equate the denominator to 0 and solve for x.
i.e
[tex]x(x^2-36) = 0[/tex]
⇒x = 0 and [tex]x^2-36 = 0[/tex]
⇒x = 0 and [tex]x^2 = 36[/tex]
or
x = 0 and [tex]x = \pm 6[/tex]
So, the domain of the function h(x) is the set of all real number except x = 0 and [tex]x = \pm 6[/tex]
Therefore, the domain of the function h(x) is:
[tex]\{x | x\neq \pm 6 , x\neq 0\}[/tex]
