Find the domain of $LaTeX: \displaystyle f(x) = \sqrt{5 x + 10} + 9$ . 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 $LaTeX: \displaystyle 5 x + 10 \geq 0$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle 5 x \geq -10$ Dividing to finish isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x \geq -2$ . The domain is $LaTeX: \displaystyle \left[-2, \infty\right)$