## Precalculus (6th Edition) Blitzer

Domain: $(-\infty,-2)\cup(6,\infty)$
Logarithmic functions are defined for positive arguments only. $f(x)=\ln(x^{2}-4x-12)$ is defined for positive values. $x^{2}-4x-12 \gt 0\quad$ Factor the trinomial -- find factors of $-12$ whose sum is $-4$; we find $-6$ and $+2.$ $(x+2)(x-6) \gt 0$ The graph of $y=x^{2}-4x-12=(x+2)(x-6)$ is a parabola opening upwards, intersecting the x-axis at $-2$ and $+6.$ We know that $y$ is positive where the graph is above the x-axis. The graph is above the x-axis before the left x-intercept $(x \lt -2)$ and to the right of the right intercept $(x \gt 6)$ Thus, the domain is: $(-\infty,-2)\cup(6,\infty)$