Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Functions: Domains and Defining Equations - Exercises - Page 487: 22

$[-2,3]\cup[4,\infty)$.

The domain requirement for $f(x)=\sqrt {(x-3)(x+2)(x-4)}$ is $(x-3)(x+2)(x-4)\geq0$ which gives $x\geq4$ (all factors are positive or one is zero), $-2\leq x\leq 3$ (only one factor is positive or zero), and in interval notation $[-2,3]\cup[4,\infty)$.