Question

Urgent help needed...............

Answer 1

The domain of the function is given by the expression in alternative B

Explanation:

The domain of a function is defined as the set of x-values for which the function is real and defined. For the given rational function, the function will not be defined if the function in the denominator assumes a value of zero.Therefore, the function will not be defined whenever; x(x^2-49)=0. Solving for x yields; x=0 and x=±7. This implies that the domain of the rational function is the set of all real numbers except where x=0 and x=±7. These are points of discontinuity

Answer 2

Option b is correct

`\ x \\eq \pm 7, x\\eq 0\`.

Explanation:

Domain is the set of all possible values of x where function is defined.

Given the function:

`h(x) = (9x)/(x(x^2-49))`

To find the domain of the given function:

Exclude the values of x, for which function is not defined

Set denominator = 0

`x(x^2-49) = 0`

By zero product property;

`x = 0` and
`x^2-49= 0`

⇒x = 0 and
`x^2 =49`

⇒x = 0 and
`x = \pm 7`

Therefore, the domain of the given function is:

`\ x \\eq \pm 7, x\\eq 0\`