Find the domain of the function. (Enter your answer using interval notation.)
h(x) = 
	root(5x − 2)
 


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

Find the domain of the function. (Enter your answer using interval notation.) h(x) = √(5x − 2)

Discover how to find the domain of the function h(x) = √(5x − 2). This problem involves solving inequalities and understanding the domain of radical functions. Suitable for high school students in Grades 9-11.

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