# Chapter 3 - Section 3.2 - Exponential Functions - Exercise Set - Page 464: 109

Domain: $(-\infty,-1)\cup(2,\infty)$

#### Work Step by Step

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: $(-\infty,-1)\cup(2,\infty)$

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