Answer:
Option b is correct
[tex]\{x | x \neq \pm 7, x\neq 0\}[/tex].
Step-by-step explanation:
Domain is the set of all possible values of x where function is defined.
Given the function:
[tex]h(x) = \frac{9x}{x(x^2-49)}[/tex]
To find the domain of the given function:
Exclude the values of x, for which function is not defined
Set denominator = 0
[tex]x(x^2-49) = 0[/tex]
By zero product property;
[tex]x = 0[/tex] and [tex]x^2-49= 0[/tex]
⇒x = 0 and [tex]x^2 =49[/tex]
⇒x = 0 and [tex]x = \pm 7[/tex]
Therefore, the domain of the given function is:
[tex]\{x | x \neq \pm 7, x\neq 0\}[/tex]
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
