Question

State the domain of the rational function. (2 points)

f(x) = six divided by quantity four minus x.


All real numbers except 6

All real numbers except 4

All real numbers except -6 and 6

All real numbers except -4 and 4

Answer 1

All real number except 4.

Explanation:

We are given that a function

`f(x)`=six divided by quantity four minus x.

We have to state the domain the rational function

`f(x)=(6)/(4-x)`

The rational function is defined for all values of x except but when x=4

Then we get denominator 4-4=0

Then ,
`f(x)=(6)/(0)=\infty`

Therefore, function is not defined at x=4.

Domain : it is defined as the set of values of x at which function is defined .

Hence, domain of given function is all real numbers except 4.

Answer 2

B) All the real numbers except 4.

Explanation:

The given rational expression f(x) =
`(6)/(4 -x)`

To find the domain of the rational function, first we have to find the restricted domain.

To find the restricted domain set the denominator equal to zero.

4 - x = 0

x = 4

The restricted domain is at x = 4.

Which means the function does not exist when x = 4. When we plug in x =4 in the rational function, we get the denominator is 0.

Therefore, the function does not exist at x =- 4.

This means except 4 all the real numbers are the domain.

Hope this will help you to understand the concept.

Answer: B) All the real numbers except 4.

Thank you.