Question

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

Answer 1

Answer: Correct Option is "C"

( - ∞ , 3) U (3, ∞ )

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.

Answer 2

ANSWER

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


EXPLANATION

The given functions are

`f(x) = x + 8`

and


`g(x) = x - 3`

The function,


`(f)/(g) = (f(x))/(g(x))`


This implies that,


`(f)/(g) = (x + 8)/(x - 3)`

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


`(f)/(g) = (x + 8)/(x - 3)`
is defined.


This function is defined if the denominator

`x - 3\\e0`



`x \\e3`


In interval form, we write this as,


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


The correct answer is C.