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

 Apr 25, 2024
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The only constraint for the domain here, is the fact that the inside of the square root also known as the radicand must be greater or equal or 0. 

 

Essentially, we get \(6-x-x^2-2x^2 \geq 0\)

 

Then, we simply solve this inequality and there's your domain. Now, I'm not going to write the entire process down for this inequality, so try solving it yourself, and give it a try. It's pretty simple. Combine the like terms to get \(-3x^2 -x + 6 \geq 0\). Plug this into the quadratic formula, and you achieve the asnwer of 

In inequality form, it would be \(-\frac{1+\sqrt{73}}{6} \leq x \leq -\frac{1-\sqrt{73}}{6}\)

In Interval Notation, it would be \([-\frac{1+\sqrt{73}}{6}, -\frac{1-\sqrt{73}}{6}]\)

 

 

Thanks!

 Apr 25, 2024

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