find the inverse for the function:

\f(x) = -3x + 15\

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

Question

find the inverse for the function:

\f(x) = -3x + 15\

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Finding Inverse Algebraically", "Linear Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Finding Inverse Algebraically", "Linear Inverse Functions" ] } ## Replace function notation with y Using the *Finding Inverse Algebraically* knowledge point $$ y = -3x + 15 $$ ## Swap variables x and y Using the *Finding Inverse Algebraically* knowledge point $$ x = -3y + 15 $$ ## Solve for y Using the *Finding Inverse Algebraically* and *Linear Inverse Functions* knowledge points $$ \begin{aligned} x - 15 &= -3y \ y &= \frac{x - 15}{-3} \ y &= -\frac{x}{3} + 5 \end{aligned} $$ ## Match with the given template Using the *Linear Inverse Functions* knowledge point $$ f^{-1}(x) = -\frac{x}{3} + 5 $$ Find the inverse for the function: $f(x) = -3x + 15$ $f^{-1}(x) = -\frac{x}{}$3 + 5 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Inverse Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Replace function notation with y

Swap variables x and y

Solve for y

Match with the given template

Answer: