If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?
StartRoot one-half x EndRoot greater-than-or-equal-to 0
One-half x greater-than-or-equal-to 0
One-half x minus 10 greater-than-or-equal-to 0
StartRoot one-half x minus 10 EndRoot + 3 greater-than-or-equal-to 0

To find the domain of a function involving a square root, the expression inside the square root must be greater than or equal to zero, as the square root of a negative number is undefined in the real number system.

Given the function:

\[
f(x) = \sqrt{\frac{1}{2}x - 10} + 3
\]

The expression inside the square root is \(\frac{1}{2}x - 10\), and this must be greater than or equal to zero:

\[
\frac{1}{2}x - 10 \geq 0
\]

This inequality ensures that the function is defined for real values of \(x\). Therefore, the correct inequality is:

\[
\frac{1}{2}x - 10 \geq 0
\]

Now, solving this inequality:

\[
\frac{1}{2}x \geq 10
\]

Multiply both sides by 2:

\[
x \geq 20
\]

Thus, the domain of \(f(x)\) is \(x \geq 20\).

### The correct inequality is:
\[
\frac{1}{2}x - 10 \geq 0
\]

### Would you like more details on solving this inequality or any other questions?

Here are some related questions you might want to explore:
1. How do you solve quadratic inequalities?
2. What is the domain of a function involving absolute value?
3. How do you graph a square root function?
4. What are common restrictions on the domain of radical functions?
5. How does adding or subtracting constants outside a square root affect the graph?

**Tip:** Always check for restrictions like square roots and denominators when finding the domain of a function!

If f(x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?

Learn how to find the domain of the function f(x) = √(1/2 x - 10) + 3 by solving the inequality inside the square root. This algebra problem covers radical functions and domain restrictions, ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation