Find the domain of the logarithmic function.
-$$f ( x ) = \log \left( \frac { x + 6 } { x - 4 } \right)$$
A) $( - \infty , - 6 ) \cup ( 4 , \infty )$
B) $( - 6,4 )$
C) $( 4 , \infty )$
D) $( - \infty , - 6 )$ (

Question

Quizplus · Accepted Answer

The domain of a logarithmic function is where the argument is positive. Here, $\frac{x+6}{x-4} > 0$. Solving this inequality gives $x < -6$ or $x > 4$. Thus, the domain is $( - \infty , - 6 ) \cup ( 4 , \infty )$.

Find the Domain of the Logarithmic Function f(x)=log⁡(x+6x−4)f ( x ) = \log \left( \frac { x + 6 } { x - 4 } \right)f(x)=log(x−4x+6​)

Find the Domain of the Logarithmic Function $f ( x ) = \log \left( \frac { x + 6 } { x - 4 } \right)$