The function given is $h(x) = \sqrt{5x - 2}$. To find the domain of this function, we need to determine for which values of $x$ the expression inside the square root is non-negative, since the square root of a negative number is not defined in the real number system.

So, we require:

$5x - 2 \geq 0$

Step 1: Solve the inequality.

$5x \geq 2$ $x \geq \frac{2}{5}$

Step 2: Domain in interval notation.

The function $h(x) = \sqrt{5x - 2}$ is defined for $x \geq \frac{2}{5}$, so the domain of the function in interval notation is:

$\left[ \frac{2}{5}, \infty \right)$

Would you like more details on the solution? Feel free to ask questions. Here are five related questions to deepen your understanding:

1. What happens if the function inside the square root is negative?
2. How would