Question

what is the domain of this square root function?

\\f(x) = \sqrt{4x - 28}\\

\\x \ge ?\\

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Domain of Radical Functions",
"Radicand Inequality"
],
"new_concepts": [],
"current_concepts": [
"Domain of Radical Functions",
"Radicand Inequality"
]
}
</pre_analysis>

<reasoning>

Set up the radicand inequality

\[
4x - 28 \ge 0
\]

Solve the inequality for x

\[

$$\begin{aligned} 4x &\ge 28 \\ x &\ge 7 \end{aligned}$$

\]
</reasoning>

<answer>
What is the domain of this square root function?
\(f(x) = \sqrt{4x - 28}\)
\(x \ge\) <blank>7</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Domain of Radical Functions"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Domain of Radical Functions",
"Radicand Inequality"
],
"new_concepts": [],
"current_concepts": [
"Domain of Radical Functions",
"Radicand Inequality"
]
}
</pre_analysis>

<reasoning>

Set up the radicand inequality

\[
4x - 28 \ge 0
\]

Solve the inequality for x

\[

$$\begin{aligned} 4x &\ge 28 \\ x &\ge 7 \end{aligned}$$

\]
</reasoning>

<answer>
What is the domain of this square root function?
\(f(x) = \sqrt{4x - 28}\)
\(x \ge\) <blank>7</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Domain of Radical Functions"
]
}
</post_analysis>