Find the domain of the function.
-$$f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$$
A) $( - \infty , 9 )$ or $( 9 , \infty )$
B) $( 9 , \infty )$
C) $( - \infty , 0 )$ or $( 0 , \infty )$
D) $( - 9 , \infty )$

Question

Quizplus · Accepted Answer

The argument of the logarithm, $(x - 9)^2$, must be greater than 0 because the base of the logarithm is positive and not equal to 1. Since squaring any real number except 0 gives a positive result, $x - 9$ can be any real number except 9. Therefore, the domain is all real numbers except 9, which is option A: $(- \infty , 9)$ or $(9 , \infty)$.

Find the Domain of the Function f(x)=log⁡4(x−9)2f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }f(x)=log4​(x−9)2

Find the Domain of the Function $f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$