4). let $f(x) = x^2 + 4$ and $g(x) = 2x$.
find the composite function $f \circ g$ and give its domain in interval notation.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Domain of a Function", "Interval Notation" ], "new_concepts": [ "Composite Functions" ], "current_concepts": [ "Composite Functions", "Domain of a Function", "Interval Notation" ] } ## Find the composite function $ (f \circ g)(x) $ $$ \begin{aligned} (f \circ g)(x) &= f(g(x)) \ &= f(2x) \ &= (2x)^2 + 4 \ &= 4x^2 + 4 \end{aligned} $$ ## Determine the domain of the composite function $$ \begin{aligned} &\text{Domain of } g(x) = 2x: \quad (-\infty, \infty) \ &\text{Domain of } f(x) = x^2 + 4: \quad (-\infty, \infty) \ &\text{Domain of } (f \circ g)(x) = 4x^2 + 4: \quad (-\infty, \infty) \end{aligned} $$ The composite function is $(f \circ g)(x) = 4x^2 + 4$, and its domain is $(-\infty, \infty)$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Composite Functions" ] }

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Find the composite function \( (f \circ g)(x) \)

Determine the domain of the composite function

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