Find the domain of $LaTeX: \displaystyle f(x) = \sqrt{- 6 x - 15} + 1$ . Write the solution in interval notation.

The domain of a radical function is the solution to the inequality radicand $LaTeX: \displaystyle \geq 0$ . The inequality is $LaTeX: \displaystyle - 6 x - 15 \geq 0$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle - 6 x \geq 15$ Dividing to finish isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x \leq - \frac{5}{2}$ . The domain is $LaTeX: \displaystyle \left(-\infty, - \frac{5}{2}\right]$