Find the domain of the function.
f left parenthesis x right parenthesis equals StartRoot 5 x minus 10 EndRoot

The given function is:

\[
f(x) = \sqrt{5x - 10}
\]

### To find the domain of this function:

1. **Identify the restriction for the square root function**: The expression inside the square root, \(5x - 10\), must be **non-negative** because the square root of a negative number is not defined in the set of real numbers.

\[
5x - 10 \geq 0
\]

2. **Solve for \(x\)**:
\[
5x \geq 10
\]
\[
x \geq \frac{10}{5}
\]
\[
x \geq 2
\]

### Domain:
The domain of \(f(x)\) is the set of \(x\)-values where \(x \geq 2\). In interval notation, the domain is:

\[
[2, \infty)
\]

Let me know if you'd like more details on this solution, and here are five related questions:

1. What is the range of \(f(x) = \sqrt{5x - 10}\)?
2. How would the domain change if the function were \(f(x) = \sqrt{-5x + 10}\)?
3. What is the domain of \(f(x) = \frac{1}{\sqrt{5x - 10}}\)?
4. How would the domain be affected if the square root function were cubed instead of squared?
5. Can this function have any complex values for certain \(x\)-values?

**Tip**: For square root functions, always check that the inside expression is non-negative to ensure the function is real-valued.

Find the domain of the function. f(x) = √(5x - 10)

Learn how to find the domain of the function f(x) = √(5x - 10). This solution explores the concept of square roots, solving inequalities, and determining the set of valid x-values. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation