Questions: Find the domain of the function. f(x)=sqrt(x-8) The domain of f(x) is . (Type your answer in interval notation.)

Solution Steps

To find the domain of the function \( f(x) = \sqrt{x-8} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative. This is because the square root function is only defined for non-negative numbers. Therefore, we solve the inequality \( x - 8 \geq 0 \).

The function given is \( f(x) = \sqrt{x-8} \). This is a square root function, and the expression inside the square root, \( x-8 \), must be non-negative for the function to be defined in the real number system.

To find the domain, we need to solve the inequality:

\[ x - 8 \geq 0 \]

Add 8 to both sides of the inequality:

\[ x \geq 8 \]

This inequality tells us that \( x \) must be greater than or equal to 8 for the function \( f(x) \) to be defined.

The solution to the inequality \( x \geq 8 \) can be expressed in interval notation as:

\[ [8, \infty) \]

Final Answer