\h(x) = x^2 + 1 \quad k(x) = x - 2\
\(h + k)(2) = \
\(h - k)(3) = \
\\text{evaluate } 3h(2) + 2k(3) = \

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{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Addition", "Function Subtraction" ], "new_concepts": [ "Linear Combinations of Functions" ], "current_concepts": [ "Function Addition", "Function Subtraction", "Linear Combinations of Functions" ] } ## Evaluate the individual functions at the required inputs $$ \begin{aligned} h(2) &= 2^2 + 1 = 5 \ k(2) &= 2 - 2 = 0 \ h(3) &= 3^2 + 1 = 10 \ k(3) &= 3 - 2 = 1 \end{aligned} $$ ## Compute the function operations $$ \begin{aligned} (h + k)(2) &= h(2) + k(2) = 5 + 0 = 5 \ (h - k)(3) &= h(3) - k(3) = 10 - 1 = 9 \end{aligned} $$ ## Evaluate the linear combination $$ 3h(2) + 2k(3) = 3(5) + 2(1) = 15 + 2 = 17 $$ ## Question 1 $ (h + k)(2) = $ 5 ## Question 2 $ (h - k)(3) = $ 9 ## Question 3 Evaluate $ 3h(2) + 2k(3) = $ 17 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the individual functions at the required inputs

Compute the function operations

Evaluate the linear combination

Answer:

Question 1

Question 2

Question 3