## Precalculus (6th Edition) Blitzer

Domain: $(-\infty,-1)\cup(2,\infty)$
Logarithmic functions are defined for positive arguments only. $f(x)=\ln(x^{2}-x-2)$ is defined when $x^{2}-x-2 \gt 0\quad$ Factor the trinomial: find factors of $-2$ whose sum is $-1$; here, we find $-2$ and $+1.$ $(x-2)(x+1) \gt 0$ The graph of $y=x^{2}-x-2=(x-2)(x+1)$ is a parabola opening upwards, intersecting the x-axis at $-1$ and $+2.$ We know tht $y$ is positive where the graph is above the x-axis. The graph is above the x-axis before the left x-intercept $(x \lt -1)$ and to the right of the right intercept $(x \gt 2)$ Domain: $(-\infty,-1)\cup(2,\infty)$