Find the domain of the function.
-$$f ( x ) = \log \left( \frac { x + 2 } { x - 8 } \right)$$
A) $( - \infty , - 2 )$
B) $( 8 , \infty )$
C) $( - \infty , - 2 ) \cup ( 8 , \infty )$
D) $( - 2,8 )$

Question

Quizplus · Accepted Answer

The argument of the logarithm function, $\frac{x + 2}{x - 8}$, must be greater than zero. This means both the numerator and denominator must be of the same sign. For $x + 2 > 0$, $x > -2$, and for $x - 8 > 0$, $x > 8$. However, when $x$ is between -2 and 8, the numerator is positive and the denominator is negative, making the fraction negative. Therefore, the domain excludes the interval $(-2, 8)$ and includes $(-\infty, -2)$ and $(8, \infty)$, making the correct domain $(-\infty, -2) \cup (8, \infty)$.

Find the Domain of the Function f(x)=log⁡(x+2x−8)f ( x ) = \log \left( \frac { x + 2 } { x - 8 } \right)f(x)=log(x−8x+2​)

Find the Domain of the Function $f ( x ) = \log \left( \frac { x + 2 } { x - 8 } \right)$