Domain

The domain must be all real numbers except for when $\sqrt{6-x-x^2-2x^2}=0$ Simplifying this, we get:

$-3x^2-x+6=0$

a = -3, b = -1, and c = 6.

$x = {1 \pm \sqrt{1+72} \over -6}$

$x=\frac{1\pm\sqrt{73}}{-6}$

The domain of the function $f(x)=\sqrt{6-x-x^2-2x^2}$ is all real numbers except $x=\frac{1+\sqrt{73}}{-6}$ and $x=\frac{1-\sqrt{73}}{-6}$.