at a movie theater, patrons earn 1 point for every $5 they spend, plus 20 bonus points on their first movie. if function (f) represents the number of points earned as a function of the total amount spent (x), which function represents the total amount spent as a function of the number of points earned?

a. (f^{-1}(x) = 0.2x + 100)
b. (f^{-1}(x) = 0.2x - 100)
c. (f^{-1}(x) = 5x + 100)
d. (f^{-1}(x) = 5x - 100)

Question

at a movie theater, patrons earn 1 point for every $5 they spend, plus 20 bonus points on their first movie. if function (f) represents the number of points earned as a function of the total amount spent (x), which function represents the total amount spent as a function of the number of points earned?

a. (f^{-1}(x) = 0.2x + 100)
b. (f^{-1}(x) = 0.2x - 100)
c. (f^{-1}(x) = 5x + 100)
d. (f^{-1}(x) = 5x - 100)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions", "Finding Inverse Functions" ], "new_concepts": [], "current_concepts": [ "Linear Modeling", "Inverse Functions", "Finding Inverse Functions" ] } ## Set up the function for points earned $$ f(x) = \frac{1}{5}x + 20 = 0.2x + 20 $$ ## Solve for x in terms of f(x) $$ \begin{aligned} y &= 0.2x + 20 \ y - 20 &= 0.2x \ x &= \frac{y - 20}{0.2} \ x &= 5(y - 20) \ x &= 5y - 100 \end{aligned} $$ ## Write the inverse function $$ f^{-1}(x) = 5x - 100 $$

A. $f^{-1}(x) = 0.2x + 100$

B. $f^{-1}(x) = 0.2x - 100$

C. $f^{-1}(x) = 5x + 100$

D. $f^{-1}(x) = 5x - 100$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the function for points earned

Solve for x in terms of f(x)

Write the inverse function

Answer: