Question

What is the domain of f/g, given f(x)=x+8 and g(x)=x-3?

Answer 1

ANSWER
$( - \infty ,3 ) \cup (3, \infty )$


EXPLANATION

The given functions are
$f(x) = x + 8$

and

$g(x) = x - 3$

The function,

$\frac{f}{g} = \frac{f(x)}{g(x)}$


This implies that,

$\frac{f}{g} = \frac{x + 8}{x - 3}$

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

$\frac{f}{g} = \frac{x + 8}{x - 3}$
is defined.


This function is defined if the denominator
$x - 3\ne0$


$x \ne3$


In interval form, we write this as,

$( - \infty ,3 ) \cup (3, \infty )$


The correct answer is C.

Answer 2

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.