Chapter 3, Polynomial and Rational Functions - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 352: 41

$D=\{x|-2

$f(x)=\sqrt{6+x-x^2}$, To get the domain, $\sqrt{6+x-x^2}\geq0$, $-x^2+x+6\geq0$, $-x^2-2x+3x+6\geq0$, $-x(x+2)+3(x+2)\geq0$, $(-x+3)(x+2)\geq0$, thus, either $-x+3\geq0, x\leq3$ or $x+2\geq0, x\geq-2$. Therefore the Domain is: $[-2,3]$.