Please help!

The domain of the function g(x)=loga(x^2-64) is

(-infinity, ) and ( ,infinity)

*** the a is the base

Question

Please help!

The domain of the function g(x)=loga(x^2-64) is

(-infinity,  ) and (  ,infinity)

*** the a is the base

mathmale · Answer

Would you mind explaining what "domain" means to you, so that I can be certain that you understand it?

mathmale · Answer

Find the domain of $$g(x)=\log_{a}(x^2-64) $$

mathmale · Answer

Can you complete the following sentence?

The values of x here MUST be such that the input of the log function is ......  "

anonymous · Answer

The domain is all values of x

trojanpoem · Answer

Log(a)  -> a here can't be either zero or negative so

a > 0

In your example we have :

log (x^2 -64)

x^2 - 64 > 0

x^2 > 64
|x| > 8

-x > 8

x > 8

x < -8

To get the domain :

x = R - [ -8, 8]

mathmale · Answer

Nice work, TrojanPoem!
Since the domain of the log function is (0, inf),
$$x^2-64 $$
must be >0.  This is equivalent to $$x^2>64. $$

mathmale · Answer

Results will be the same as TrojanPoem found.
I would prefer to write the domain as$$(-\infty,-8) U (8,\infty).$$