Find the domain of the function.

yequalsStartRoot 2 x minus 7 EndRoot

The function is given as:

\[
y = \sqrt{2x - 7}
\]

To determine the domain of this function, we need to ensure that the expression inside the square root is non-negative, because the square root of a negative number is undefined in the set of real numbers.

The condition for the square root to be defined is:

\[
2x - 7 \geq 0
\]

Now, solve for \(x\):

\[
2x \geq 7
\]

\[
x \geq \frac{7}{2}
\]

Thus, the domain of the function is all \(x\) such that:

\[
x \geq \frac{7}{2}
\]

In interval notation, the domain is:

\[
\left[ \frac{7}{2}, \infty \right)
\]

Would you like further clarification or have any other questions?

Here are some related questions:
1. What is the range of the function \( y = \sqrt{2x - 7} \)?
2. How would the domain change if the function were \( y = \sqrt{3x - 5} \)?
3. What is the domain of \( y = \frac{1}{\sqrt{2x - 7}} \)?
4. How would you find the domain of a logarithmic function like \( y = \log(2x - 7) \)?
5. What is the domain of the function \( y = \sqrt{(x^2 - 4)} \)?

**Tip:** Always check the conditions under which a square root, logarithmic, or rational function is defined, as these often have restricted domains.

Find the domain of the function y = sqrt(2x - 7).

Learn how to find the domain of the square root function y = sqrt(2x - 7). This problem involves algebraic manipulation and understanding the conditions for a square root function to be defined. Suitable for students in Grades 9-11.

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