The problem asks to find the domain of the function $f(x) = \sqrt{x - 8}$.

Step-by-Step Solution:

1. Understand the Function: The function given is $f(x) = \sqrt{x - 8}$. Since the square root function is only defined for non-negative values, the expression inside the square root, $x - 8$, must be greater than or equal to zero.

2. Set Up the Inequality: $x - 8 \geq 0$

3. Solve the Inequality: Add 8 to both sides to isolate $x$: $x \geq 8$

4. Interpret the Domain: The domain of $f(x)$ is all $x$ values where $x \geq 8$.

5. Express in Interval Notation: The domain in interval notation is: $[8, \infty)$

Final Answer:

The domain of $f(x) = \sqrt{x - 8}$ is $[8, \infty)$.

Would you like more details on this problem, or do you have any other questions?

Related Questions:

1. What is the range of $f(x) = \sqrt{x - 8}$?
2. How would the domain change if the function were $f(x) = \sqrt{8 - x}$?
3. What is the domain of $f(x) = \sqrt{(x - 8)(x + 2)}$?
4. Can you find the domain and range of the function $f(x) = \sqrt{4x - 16}$?
5. How does adding a constant to the function $f(x) = \sqrt{x - 8}$ affect its domain?

Tip:

When working with square root functions, always check the expression inside the root to ensure it is non-negative, as this determines the domain of the function.