Find the domain of the following function: lower f left parenthesis x right parenthesis equals Start Root x minus 4 End Root. Write your answer in interval notation.

Question

(1 point)
Responses

left parenthesis negative 4 comma infinity right parenthesis
Image with alt text: left parenthesis negative 4 comma infinity right parenthesis

left parenthesis 4 comma infinity right parenthesis
Image with alt text: left parenthesis 4 comma infinity right parenthesis

left bracket negative 4 comma infinity right parenthesis
Image with alt text: left bracket negative 4 comma infinity right parenthesis

Answer 1

To find the domain of the function \( f(x) = \sqrt{x - 4} \), we need to determine for which values of \( x \) the expression inside the square root is non-negative, since the square root function is only defined for non-negative arguments.

Set up the inequality:

\[ x - 4 \geq 0 \]

Solving for \( x \):

\[ x \geq 4 \]

This means that \( x \) must be greater than or equal to 4. Therefore, the domain of the function \( f(x) \) in interval notation is:

\[ [4, \infty) \]

None of your provided responses exactly match this answer. However, the proper notation for the domain of \( f(x) \) with the included endpoint (4) is:

Answer: \([4, \infty)\)