if $f(x) = 3x^2$ and $g(x) = 4x^3 + 1$, what is the degree of $(f \circ g)(x)$?

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Question

if $f(x) = 3x^2$ and $g(x) = 4x^3 + 1$, what is the degree of $(f \circ g)(x)$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Composite Functions" ], "new_concepts": [ "Degree of Composite Functions" ], "current_concepts": [ "Composite Functions", "Degree of Composite Functions" ] } ## Express the composite function $$ (f \circ g)(x) = f(g(x)) = 3(4x^3 + 1)^2 $$ ## Expand the expression to find the leading term $$ (f \circ g)(x) = 3(16x^6 + 8x^3 + 1) = 48x^6 + 24x^3 + 3 $$ ## Determine the degree of the polynomial $$ \text{Degree} = 6 $$

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

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QUESTION IMAGE

Question

Explanation:

Express the composite function

Expand the expression to find the leading term

Determine the degree of the polynomial

Answer: