Question

Determine the domain of the function

Answer 1

Answer:

Option B is correct.

The domain of the function h(x) is: $\{x | x\neq \pm 6 , x\neq 0\}$

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:

$h(x) = \frac{9x}{x(x^2-36)}$

To find the excluded value in the domain of the function.

equate the denominator to 0 and solve for x.

i.e

$x(x^2-36) = 0$

⇒x = 0 and $x^2-36 = 0$

⇒x = 0 and $x^2 = 36$

or

x = 0 and $x = \pm 6$

So, the domain of the function h(x) is the set of all real number except x = 0 and $x = \pm 6$

Therefore, the domain of the function h(x) is:

$\{x | x\neq \pm 6 , x\neq 0\}$

Answer 2

Answer:

Choice b is correct.

Step-by-step explanation:

We have to find the domain of the given function.

The given function is 9x/x(x²-36).

Domain is the all possible values of x for which the function is defined.

so the function is undefined when x(x²-36) = 0.

So,

x(x²-36) =0

either x = 0 or (x² -36) =0

x=0 or x²= 36

x=0 or x = ±6

So, the domain of function is the set of real numbers except x=0 and x = ±6.