Find the domain of the function below.
$$f ( x ) = \ln \left( \frac { x + 3 } { x - 5 } \right)$$
A) $( - \infty , 5 )$
B) $( - \infty , - 3 )$
C) $( - 3 , \infty )$
D) $( 5 , \infty )$
E) $( - \infty , - 3 ) \cup ( 5 , \infty )$

Question

Quizplus · Accepted Answer

In order for the function to be well-defined, we must have: $$\frac{x+3}{x-5}>0$$ This inequality is satisfied when $x+3$ and $x-5$ have the same sign (both positive or both negative). Thus, the domain consists of all $x$ such that either $x+3>0$ and $x-5>0$ (i.e. $x>5$), or $x+3<0$ and $x-5<0$ (i.e. $x<-3$). Therefore, the domain is given by: $$\boxed{(-\infty,-3)\cup(5,\infty)}$$

Find the Domain of the Function Below f(x)=ln⁡(x+3x−5)f ( x ) = \ln \left( \frac { x + 3 } { x - 5 } \right)f(x)=ln(x−5x+3​)

Find the Domain of the Function Below $f ( x ) = \ln \left( \frac { x + 3 } { x - 5 } \right)$