Write the domain in interval notation.
-$$f ( x ) = \ln \left( x ^ { 2 } + 8 x + 12 \right)$$
A) $( - \infty , - 6 ) \cup ( - 2 , \infty )$
B) $( - \infty , 2 ) \cup ( 6 , \infty )$
C) $( - \infty , 2 ] \cup [ 6 , \infty )$
D) $[ - 6 , - 2 ]$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \ln(x^2 + 8x + 12)$ is determined by the requirement that the argument of the logarithm, $x^2 + 8x + 12$, must be greater than zero. Factoring the quadratic expression gives $(x+6)(x+2) > 0$. Solving this inequality, we find that the solution is $x < -6$ or $x > -2$, which corresponds to the interval notation $(- \infty , - 6 ) \cup ( - 2 , \infty )$.

Write the Domain in Interval Notation f(x)=ln⁡(x2+8x+12)f ( x ) = \ln \left( x ^ { 2 } + 8 x + 12 \right)f(x)=ln(x2+8x+12)

Write the Domain in Interval Notation $f ( x ) = \ln \left( x ^ { 2 } + 8 x + 12 \right)$