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To determine which values of \( x \) must be excluded from the domain of the function \( f(x) = \sqrt{x - 6} \), we need to ensure that the expression inside the square root is non-negative because the square root of a negative number is not defined in the set of real numbers.

Thus, we set up the inequality:
\[ x - 6 \geq 0 \]

Solving for \( x \):
\[ x \geq 6 \]

Therefore, the values of \( x \) that must be excluded from the domain of \( f \) are those less than 6. In other words, \( x \) must be at least 6 for \( f(x) \) to be defined. Hence, the domain of \( f \) is:
\[ [6, \infty) \]

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:
1. What is the range of the function \( f(x) = \sqrt{x - 6} \)?
2. How would the domain change if the function were \( f(x) = \sqrt{6 - x} \)?
3. What is the domain of the function \( g(x) = \sqrt{x^2 - 9} \)?
4. How do you find the domain of a function involving a logarithm, such as \( h(x) = \ln(x - 6) \)?
5. How do you determine the domain and range of a rational function?

**Tip:** When finding the domain of a function, always look for values that could make the function undefined, such as causing a division by zero or taking the square root of a negative number.

State which values of x must be excluded from the domain of f, where f(x) = sqrt(x - 6).

Learn how to determine the domain of the function f(x) = sqrt(x - 6). Understand why x must be greater than or equal to 6 and how square root functions behave. Suitable for students in Grades 8-10.

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