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 \(x=\frac{1-\sqrt{73}}{-6}\).