https://file.aiquickdraw.com/mathbot/file/1724787946163fyfewaem.jpg

The image shows a question asking for the domain and range of the function \( f(x) = \sqrt{x - 4} \).

### Explanation:

1. **Domain:** The domain of the function \( f(x) = \sqrt{x - 4} \) consists of all values of \( x \) for which the expression under the square root is non-negative (because the square root of a negative number is not a real number). Therefore, we set \( x - 4 \geq 0 \), which gives \( x \geq 4 \). So, the domain is \( [4, \infty) \).

2. **Range:** The range of the function is determined by the output values of \( f(x) \). Since the square root function produces non-negative outputs, and the smallest value inside the square root is 0 (when \( x = 4 \)), the range of \( f(x) = \sqrt{x - 4} \) is \( [0, \infty) \).

### Answer:
- The correct answer, as indicated in the image, is **Option A**:
  - **Domain:** \( [4, \infty) \)
  - **Range:** \( [0, \infty) \)

Would you like further details on the function's domain and range, or do you have any other questions?

### Related Questions:
1. How would the domain and range change if the function were \( f(x) = \sqrt{4 - x} \)?
2. What is the domain of the function \( f(x) = \frac{1}{\sqrt{x - 4}} \)?
3. How do you find the range of a quadratic function?
4. What is the difference between the domain and range of a function?
5. How would you graph the function \( f(x) = \sqrt{x - 4} \)?

### Tip:
When determining the domain of a function involving a square root, always consider the expression under the root and set it greater than or equal to zero to find the permissible values of \( x \).

Explore the domain and range of the function f(x) = sqrt(x - 4) in detail with clear explanations and examples. Learn how to determine the permissible values of x and the possible outputs of the function. Suitable for advanced high school students and college-level learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation