Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer:

Option b is correct

$\{x | x \neq \pm 7, x\neq 0\}$.

Step-by-step explanation:

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

Given the function:

$h(x) = \frac{9x}{x(x^2-49)}$

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:

$\{x | x \neq \pm 7, x\neq 0\}$