Find the domain of the function. $h ( x ) = \ln \left( x ^ { 2 } - 9 \right)$
A) $( - \infty , \infty )$
B) $( - \infty , - 3 ) \cup ( 3 , \infty )$
C) $( - 3 , \infty )$
D) $( - \infty , - 9 ) \cup ( 9 , \infty )$
E) none of these

Question

Quizplus · Accepted Answer

The domain of a logarithmic function is restricted to the values inside the parentheses, which must be greater than zero. Therefore, we must solve the inequality $x^2-9>0$, which factors as $(x+3)(x-3)>0$. The critical points are $x=-3$ and $x=3$. We test the intervals between these points and outside them to find that the solution is $(-\infty,-3)\cup(3,\infty)$.

Find the Domain of the Function h(x)=ln⁡(x2−9)h ( x ) = \ln \left( x ^ { 2 } - 9 \right)h(x)=ln(x2−9)

Find the Domain of the Function $h ( x ) = \ln \left( x ^ { 2 } - 9 \right)$