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 logarithm of 0 or a negative number is undefined. Since squaring any non-zero number gives a positive result, $(x - 9)^2 > 0$ for all $x$ except $x = 9$. Thus, the domain is all real numbers except 9, which corresponds to $( - \infty , 9 )$ 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 $f ( x ) = \log _ { 4 } ( x - 9 ) ^ { 2 }$