Write the domain in interval notation.
-$$f ( x ) = \log _ { 9 } \left( \frac { x - 5 } { x + 8 } \right)$$
A) $( - \infty , \infty )$
B) $( - 8,5 ]$
C) $( - 8,5 )$
D) $( - \infty , - 8 ) \cup ( 5 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a logarithmic function is all the values of $x$ for which the argument of the logarithm is greater than zero. For the function $f(x) = \log_9\left(\frac{x - 5}{x + 8}\right)$, the argument $\frac{x - 5}{x + 8}$ must be greater than zero. This inequality is true when $x > 5$ or $x < -8$, which excludes the interval $[-8, 5]$. Therefore, the domain is $(-\infty, -8) \cup (5, \infty)$.

Write the Domain in Interval Notation f(x)=log⁡9(x−5x+8)f ( x ) = \log _ { 9 } \left( \frac { x - 5 } { x + 8 } \right)f(x)=log9​(x+8x−5​)

Write the Domain in Interval Notation $f ( x ) = \log _ { 9 } \left( \frac { x - 5 } { x + 8 } \right)$