Question

find the inverse for the function:

\\f(x) = -5x + 20\\

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

Explanation:

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<reasoning>

Set the function equal to y

\[
y = -5x + 20
\]

Swap variables and solve for y

\[

$$\begin{aligned} x &= -5y + 20 \\ x - 20 &= -5y \\ y &= -\frac{x - 20}{5} \\ y &= -\frac{x}{5} + 4 \end{aligned}$$

\]

Identify the missing values

\[
f^{-1}(x) = -\frac{x}{5} + 4
\]
</reasoning>

<answer>
Find the inverse for the function:
\(f(x) = -5x + 20\)

\(f^{-1}(x) = -\frac{x}{<blank>5</blank>} + <blank>4</blank>\)
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Inverse Functions"
]
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Answer:

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}
</pre_analysis>

<reasoning>

Set the function equal to y

\[
y = -5x + 20
\]

Swap variables and solve for y

\[

$$\begin{aligned} x &= -5y + 20 \\ x - 20 &= -5y \\ y &= -\frac{x - 20}{5} \\ y &= -\frac{x}{5} + 4 \end{aligned}$$

\]

Identify the missing values

\[
f^{-1}(x) = -\frac{x}{5} + 4
\]
</reasoning>

<answer>
Find the inverse for the function:
\(f(x) = -5x + 20\)

\(f^{-1}(x) = -\frac{x}{<blank>5</blank>} + <blank>4</blank>\)
</answer>

<post_analysis>
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"subject": "Mathematics",
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"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Inverse Functions"
]
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