Question

Determine the domain of the function

Answer 1

Choice b is correct.

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.

Answer 2

Option B is correct.

The domain of the function h(x) is:
`\x`

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) = (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`