anonymous
  • anonymous
Please help! The domain of the function g(x)=loga(x^2-64) is (-infinity, ) and ( ,infinity) *** the a is the base
Algebra
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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mathmale
  • mathmale
Would you mind explaining what "domain" means to you, so that I can be certain that you understand it?
mathmale
  • mathmale
Find the domain of \[g(x)=\log_{a}(x^2-64) \]
mathmale
  • mathmale
Can you complete the following sentence? The values of x here MUST be such that the input of the log function is ...... "

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anonymous
  • anonymous
The domain is all values of x
TrojanPoem
  • TrojanPoem
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
  • mathmale
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
  • mathmale
Results will be the same as TrojanPoem found. I would prefer to write the domain as\[(-\infty,-8) U (8,\infty).\]

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