Find the domain of the function.
-$$f ( x ) = \log _ { 10 } \left( \frac { x + 8 } { x - 8 } \right)$$
A) $( 8 , \infty )$
B) $( - \infty , - 8 ) \cup ( 8 , \infty )$
C) $( - \infty , - 8 )$
D) $( - 8,8 )$

Question

Quizplus · Accepted Answer

The argument of the logarithm function, $\frac{x + 8}{x - 8}$, must be greater than zero. This means both the numerator and denominator must be of the same sign. For $x > 8$, both are positive, and for $x < -8$, both are negative, making the fraction positive in both cases. Thus, the domain excludes the interval $(-8, 8)$ but includes everything else, which is $(- \infty, -8) \cup (8, \infty)$.

Find the Domain of the Function f(x)=log⁡10(x+8x−8)f ( x ) = \log _ { 10 } \left( \frac { x + 8 } { x - 8 } \right)f(x)=log10​(x−8x+8​)

Find the Domain of the Function $f ( x ) = \log _ { 10 } \left( \frac { x + 8 } { x - 8 } \right)$