Question
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.
(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
(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
Answers
GPT-4o mini
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:** \([4, \infty)\)
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:** \([4, \infty)\)