Question

if \\(f(x) = 4x\\) and \\(g(x) = 2x - 1\\), what is \\(g(f(-2))\\)?

-17
-13
-8
-5

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Function Composition",
"Composite Functions"
],
"new_concepts": [],
"current_concepts": [
"Function Composition",
"Composite Functions"
]
}
</pre_analysis>

<reasoning>

Evaluate the inner function at the given input

\[
f(-2) = 4(-2) = -8
\]

Evaluate the outer function at the resulting value

\[
g(f(-2)) = g(-8) = 2(-8) - 1 = -16 - 1 = -17
\]
</reasoning>

<answer>
<mcq-correct>(A) \(-17\)</mcq-correct>
<mcq-option>(B) \(-13\)</mcq-option>
<mcq-option>(C) \(-8\)</mcq-option>
<mcq-option>(D) \(-5\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Function Composition"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Function Composition",
"Composite Functions"
],
"new_concepts": [],
"current_concepts": [
"Function Composition",
"Composite Functions"
]
}
</pre_analysis>

<reasoning>

Evaluate the inner function at the given input

\[
f(-2) = 4(-2) = -8
\]

Evaluate the outer function at the resulting value

\[
g(f(-2)) = g(-8) = 2(-8) - 1 = -16 - 1 = -17
\]
</reasoning>

<answer>
<mcq-correct>(A) \(-17\)</mcq-correct>
<mcq-option>(B) \(-13\)</mcq-option>
<mcq-option>(C) \(-8\)</mcq-option>
<mcq-option>(D) \(-5\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Function Composition"
]
}
</post_analysis>