Question

find the inverse for the function:

\\f(x) = 2x - 26\\

\\f^{-1}(x) = \frac{x}{?} + \\

Explanation:

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"Linear Inverse Functions"
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</pre_analysis>

<reasoning>

Set up the equation

\[
y = 2x - 26
\]

Swap variables and solve for y

\[

$$\begin{aligned} x &= 2y - 26 \\ x + 26 &= 2y \\ y &= \frac{x + 26}{2} \end{aligned}$$

\]

Separate the terms

\[
f^{-1}(x) = \frac{x}{2} + 13
\]
</reasoning>

<answer>
Find the inverse for the function:
\(f(x) = 2x - 26\)
\(f^{-1}(x) = \frac{x}{}\)<blank>2</blank> + <blank>13</blank>
</answer>

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

Answer:

<pre_analysis>
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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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"Linear Inverse Functions"
],
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"Linear Inverse Functions"
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}
</pre_analysis>

<reasoning>

Set up the equation

\[
y = 2x - 26
\]

Swap variables and solve for y

\[

$$\begin{aligned} x &= 2y - 26 \\ x + 26 &= 2y \\ y &= \frac{x + 26}{2} \end{aligned}$$

\]

Separate the terms

\[
f^{-1}(x) = \frac{x}{2} + 13
\]
</reasoning>

<answer>
Find the inverse for the function:
\(f(x) = 2x - 26\)
\(f^{-1}(x) = \frac{x}{}\)<blank>2</blank> + <blank>13</blank>
</answer>

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