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The function given is \( h(x) = \sqrt{4x - 5} \). To find the domain of this function, we need to determine the values of \( x \) that make the expression under the square root non-negative. 

Since the square root function is only defined for non-negative numbers, we require:

\[
4x - 5 \geq 0
\]

### Step-by-step solution:

1. Solve for \( x \):
   \[
   4x - 5 \geq 0
   \]
   \[
   4x \geq 5
   \]
   \[
   x \geq \frac{5}{4}
   \]

Thus, the domain of the function is all values of \( x \) such that \( x \geq \frac{5}{4} \).

### Interval notation:
\[
\left[ \frac{5}{4}, \infty \right)
\]

Would you like more details or have any questions about this? Here are some additional related questions:

1. How would the domain change if it were \( \sqrt{4x + 5} \)?
2. What is the range of \( h(x) = \sqrt{4x - 5} \)?
3. How do you find the domain of a rational function?
4. What would the graph of this function look like?
5. How do square root functions affect the overall domain and range?

**Tip**: Always look for restrictions like square roots or divisions in functions when determining their domain.

Find the domain of the function h(x) = sqrt(4x - 5). (Enter your answer using interval notation.)

Learn how to find the domain of the function h(x) = sqrt(4x - 5) using interval notation. This problem involves determining the values of x that keep the expression under the square root non-negative. Suitable for students in Grades 9-11.

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