Find the domain of $LaTeX: \displaystyle f(x) = \sqrt{7 x + 1} + 2$ . 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 $LaTeX: \displaystyle 7 x + 1 \geq 0$ . Isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle 7 x \geq -1$ Dividing to finish isolating $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x \geq - \frac{1}{7}$ . The domain is $LaTeX: \displaystyle \left[- \frac{1}{7}, \infty\right)$