if $f(x) = 3x + 2$ and $g(x) = x^2 + 1$, which expression is equivalent to $(f \circ g)(x)$?

$(3x + 2)(x^2 + 1)$
$3x^2 + 1 + 2$
$(3x + 2)^2 + 1$
$3(x^2 + 1) + 2$

Question

if $f(x) = 3x + 2$ and $g(x) = x^2 + 1$, which expression is equivalent to $(f \circ g)(x)$?

$(3x + 2)(x^2 + 1)$
$3x^2 + 1 + 2$
$(3x + 2)^2 + 1$
$3(x^2 + 1) + 2$

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": [], "current_concepts": [ "Composite Functions" ] } ## Define the composite function $$ (f \circ g)(x) = f(g(x)) $$ ## Substitute g(x) into f(x) $$ \begin{aligned} f(x) &= 3x + 2 \ g(x) &= x^2 + 1 \ f(g(x)) &= 3(g(x)) + 2 \ &= 3(x^2 + 1) + 2 \end{aligned} $$

(A) $(3x + 2)(x^2 + 1)$

(B) $3x^2 + 1 + 2$

(C) $(3x + 2)^2 + 1$

(D) $3(x^2 + 1) + 2$

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

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Question

Explanation:

Define the composite function

Substitute g(x) into f(x)

Answer: