Question

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

Answer 1

Answer:

All real number except 4.

Step-by-step 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

$f(x)=\frac{6}{4-x}$

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

Then we get denominator 4-4=0

Then , $f(x)=\frac{6}{0}=\infty$

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

Answer:

B) All the real numbers except 4.

Step-by-step explanation:

The given rational expression f(x) = $\frac{6}{4 -x}$

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.