Find the domain of $LaTeX: \displaystyle f(x) = \sqrt{19 - 9 x} + 19$ . 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 $LaTeX: \displaystyle 19 - 9 x \geq 0$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle - 9 x \geq -19$ Dividing to finish isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x \leq \frac{19}{9}$ . The domain is $LaTeX: \displaystyle \left(-\infty, \frac{19}{9}\right]$