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ANSWER
[tex]( - \infty ,3 ) \cup (3, \infty )[/tex]


EXPLANATION

The given functions are
[tex]f(x) = x + 8[/tex]

and

[tex]g(x) = x - 3[/tex]

The function,

[tex] \frac{f}{g} = \frac{f(x)}{g(x)} [/tex]


This implies that,

[tex] \frac{f}{g} = \frac{x + 8}{x - 3} [/tex]

The domain of this rational function refers to all values of x for which

[tex] \frac{f}{g} = \frac{x + 8}{x - 3} [/tex]
is defined.


This function is defined if the denominator
[tex]x - 3\ne0[/tex]


[tex]x \ne3[/tex]


In interval form, we write this as,

[tex]( - \infty ,3 ) \cup (3, \infty )[/tex]


The correct answer is C.

Answer: Correct Option is "C"

( - ∞ , 3) U (3, ∞ )


Step-by-step explanation:


The function f/g is defined as

( x + 8) / (x -3)


Domain of the function is the set of values which the independent variable can assume.


Clearly in the above function x cannot assume the value 3, otherwise the function would become undefined.


So domain of the function is

( - ∞ , 3) U (3, ∞ )


Hope it helps.


Thank you.

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