domain

Find the domain of the function \(f(x) = \sqrt{6-x-x^2-2x^2}\) .

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\(f(x) = \sqrt{6-x-x^2-2x^2}\\ -3x^2-x+6=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {1 \pm \sqrt{1+4\cdot 3\cdot 6} \over -2\cdot 3}\\ \color{blue}x\in \{-1.591,1.257\}\)

The domain of the function \(f(x) = \sqrt{6-x-x^2-2x^2}\)  goes from -1.591 to 1.257.

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