# What is the domain of sqrt(3x^2-7x-6)?

Dec 27, 2016

Factor under the square root.

$y = \sqrt{3 {x}^{2} - 9 x + 2 x - 6}$

$y = \sqrt{3 x \left(x - 3\right) + 2 \left(x - 3\right)}$

$y = \sqrt{\left(3 x + 2\right) \left(x - 3\right)}$

Set the relation to $0$ and solve for $x$.

$x = - \frac{2}{3} \mathmr{and} 3$

Use test points to check when the function will be negative and when it will be positive. You will find that the number under the square root will always be positive except over the interval $- \frac{2}{3} < x < 3$.

The domain is therefore $\left(- \infty , - \frac{2}{3}\right]$, $\left[3 , \infty\right)$.

Hopefully this helps!
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