3. given $f(x) = x^2 + 3$ and $g(x) = \sqrt{x - 3}$. find $f(4)$, $g(12)$ and $f(w+3)$ a5

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation", "Simplifying Radicals", "Algebraic Expansion" ], "new_concepts": [ "Composite Function Evaluation" ], "current_concepts": [ "Function Evaluation", "Simplifying Radicals", "Algebraic Expansion" ] } ## Evaluate f(4) Using the *Function Evaluation* knowledge point $$ \begin{aligned} f(x) &= x^2 + 3 \ f(4) &= 4^2 + 3 \ f(4) &= 16 + 3 \ f(4) &= 19 \end{aligned} $$ ## Evaluate g(12) Using the *Function Evaluation* and *Simplifying Radicals* knowledge points $$ \begin{aligned} g(x) &= \sqrt{x - 3} \ g(12) &= \sqrt{12 - 3} \ g(12) &= \sqrt{9} \ g(12) &= 3 \end{aligned} $$ ## Evaluate f(w+3) Using the *Function Evaluation* and *Algebraic Expansion* knowledge points $$ \begin{aligned} f(x) &= x^2 + 3 \ f(w+3) &= (w+3)^2 + 3 \ f(w+3) &= (w^2 + 6w + 9) + 3 \ f(w+3) &= w^2 + 6w + 12 \end{aligned} $$ $f(4) = 19$, $g(12) = 3$, and $f(w+3) = w^2 + 6w + 12$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

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Explanation:

Evaluate f(4)

Evaluate g(12)

Evaluate f(w+3)

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