given: $f(x) = 2x + 5$ and $g(x) = x^2$ and $h(x) = -2x$

$h(g(f(x))) = \underline{\quad} x^2 + \underline{\quad} x + \underline{\quad}$

Question

given: $f(x) = 2x + 5$ and $g(x) = x^2$ and $h(x) = -2x$

$h(g(f(x))) = \underline{\quad} x^2 + \underline{\quad} x + \underline{\quad}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Composite Functions", "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Composite Functions", "Polynomial Operations" ] } ## Evaluate the innermost function Using the **Composite Functions** knowledge point $$ f(x) = 2x + 5 $$ ## Substitute into the middle function Using the **Composite Functions** and **Polynomial Operations** knowledge points $$ \begin{aligned} g(f(x)) &= (2x + 5)^2 \ &= 4x^2 + 20x + 25 \end{aligned} $$ ## Substitute into the outermost function Using the **Composite Functions** and **Polynomial Operations** knowledge points $$ \begin{aligned} h(g(f(x))) &= -2(4x^2 + 20x + 25) \ &= -8x^2 - 40x - 50 \end{aligned} $$ Given: $f(x) = 2x + 5$ and $g(x) = x^2$ and $h(x) = -2x$ $h(g(f(x))) =$ $-8$ $x^2 +$ $-40$ $x +$ $-50$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Composite Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the innermost function

Substitute into the middle function

Substitute into the outermost function

Answer: