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

The domain of the function is determined by the conditions under which the argument of the logarithm, $\frac{x + 3}{x - 5}$, is positive. This fraction is positive when both the numerator and denominator are positive or both are negative. This happens when $x > -3$ and $x < 5$, or when $x > 5$. Therefore, the domain excludes the interval $(-3, 5)$ but includes everything else, leading to the correct answer $(-\infty, -3) \cup (5, \infty)$.

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 $f ( x ) = \ln \left( \frac { x + 3 } { x - 5 } \right)$