SOLUTION: Please check my work for the domain of: f(x)=log_2(x+4)+log_2(x+6) I set up a table of signs to solve this, please tell me if there is a better way to do this. <pre> ____

Algebra ->  Functions -> SOLUTION: Please check my work for the domain of: f(x)=log_2(x+4)+log_2(x+6) I set up a table of signs to solve this, please tell me if there is a better way to do this. <pre> ____      Log On


   

Question 916916: Please check my work for the domain of:
f(x)=log_2(x+4)+log_2(x+6)
I set up a table of signs to solve this, please tell me if there is a better way to do this. 
_____|-∞|-6|__|-4  |-∞ |
.(x+4)|  -  | - | -  | o   | + |
(x+6)| -   |o |+| +  | + |
answ| +|X| - | 0   | + |

therefore the domain is: (-∞,-4) U (-4,∞)
Is this correct?
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Values of x less than or equal to -4 will not work because x+4 will either be 0 or negative. Also, x+6 is likely to be negative as well.

Keep in mind that the argument of a log, the stuff inside the log, must be positive.

So (-∞,-4) is NOT part of the domain.

The answer is simply (-4,∞)