Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 9 } ( x + 1 ) ^ { 2 }$$
A) $( - 1 , \infty )$
B) $( - \infty , 0 )$ or $( 0 , \infty )$
C) $( - \infty , - 1 )$ or $( - 1 , \infty )$
D) $( 1 , \infty )$

Question

Quizplus · Accepted Answer

The expression inside the logarithm $(x + 1)^2$ must be greater than 0. Since $(x + 1)^2$ is always non-negative and equals 0 when $x = -1$, the domain is all real numbers except $x = -1$, which is $(-\infty, -1) \cup (-1, \infty)$.

Find the Domain of the Logarithmic Function f(x)=log⁡9(x+1)2f ( x ) = \log _ { 9 } ( x + 1 ) ^ { 2 }f(x)=log9​(x+1)2

Find the Domain of the Logarithmic Function $f ( x ) = \log _ { 9 } ( x + 1 ) ^ { 2 }$