Find the domain of the logarithmic function.
-$$f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right)$$
A) $( - \infty , 2 ) \cup ( 6 , \infty )$
B) $( - 2,6 )$
C) $( 6 , \infty )$
D) $( - \infty , - 2 )$ (

Question

Quizplus · Accepted Answer

For the argument of the logarithmic function to be real, we need:
$$x^2 - 8x + 12 > 0$$
Solving this quadratic inequality, we get:
$$x \in ( - \infty , 2 ) \cup ( 6 , \infty )$$
Since the logarithmic function is only defined for positive arguments, we need to further restrict the domain to:
$$x \in (2, 6)$$
Therefore, the domain of the given function is:
$$(2, 6)$$
which is equivalent to answer A.

Find the Domain of the Logarithmic Function f(x)=log⁡(x2−8x+12)f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right)f(x)=log(x2−8x+12)

Find the Domain of the Logarithmic Function $f ( x ) = \log \left( x ^ { 2 } - 8 x + 12 \right)$