find the inverse for the function:

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

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

Question

find the inverse for the function:

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Inverse Algebraically", "Linear Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Finding Inverse Algebraically", "Linear Inverse Functions" ] } ## 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 $$ f^{-1}(x) = -\frac{x}{5} + 4 $$ Find the inverse for the function: $f(x) = -5x + 20$ $f^{-1}(x) = -\frac{x}{5} + 4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inverse Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set the function equal to y

Swap variables and solve for y

Identify the missing values

Answer: