Find the domain of the function below.
$$f ( x ) = \ln \left( \frac { x - 4 } { x + 5 } \right)$$
A) $( - \infty , 4 )$
B) $( - \infty , - 5 )$
C) $( - 5 , \infty )$
D) $( 4 , \infty )$
E) $( - \infty , - 5 ) \cup ( 4 , \infty )$

Question

Quizplus · Accepted Answer

The argument of the logarithm function, $\frac{x - 4}{x + 5}$, must be greater than zero. This means $x - 4$ and $x + 5$ must have the same sign. The critical points are $x = 4$ and $x = -5$, dividing the real line into three intervals. Testing values from each interval in the inequality $\frac{x - 4}{x + 5} > 0$, we find that the inequality holds for $x < -5$ and $x > 4$, hence the domain is $(-\infty, -5) \cup (4, \infty)$.

Find the Domain of the Function Below f(x)=ln⁡(x−4x+5)f ( x ) = \ln \left( \frac { x - 4 } { x + 5 } \right)f(x)=ln(x+5x−4​)

Find the Domain of the Function Below $f ( x ) = \ln \left( \frac { x - 4 } { x + 5 } \right)$