(9x)/(4-(sqrt(6x-38)))

Question

find the domain

 

Answer 1

6x - 38 must be greater than 0 too, because otherwise taking the square root of a negative number.

 

Check out this graph:

 

https://www.desmos.com/calculator/qgvcaurvrk

 

 

Answer 2

Hi, Jessica.

Okay, so you need to find the domain. You need to show that there cannot be an answer with a denominator of 0.

 

So, let's evaluate the denominator:

 

4 - √(6x - 38)

 

This cannot be equal to 0 , so let's solve for zero and find where the solution does not exist.

 

4 - √(6x - 38) = 0

 

4 = √(6x - 38)

16 = 6x - 38

6x = 54

x = 9

 

So, at x = 9, there is not solution, therefore the domain is:

 

x = the set of all real numbers except x = 9