express the given function h as a composition of two functions f and g so that $h(x) = (f \circ g)(x)$, where one of the functions is $6x - 9$.

\h(x) = (6x - 9)^8\

$f(x) = x^8$

$g(x) = \square$

Question

express the given function h as a composition of two functions f and g so that $h(x) = (f \circ g)(x)$, where one of the functions is $6x - 9$.

\h(x) = (6x - 9)^8\

$f(x) = x^8$

$g(x) = \square$

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": [ "Function Composition" ], "new_concepts": [], "current_concepts": [ "Function Composition" ] } ## Identify the inner and outer functions Using the *Function Composition* knowledge point $$ \begin{aligned} &h(x) = (f \circ g)(x) = f(g(x))\ &h(x) = (6x - 9)^8\ &f(x) = x^8\ &f(g(x)) = (g(x))^8 = (6x - 9)^8 \implies g(x) = 6x - 9 \end{aligned} $$ Express the given function h as a composition of two functions f and g so that $h(x) = (f \circ g)(x)$, where one of the functions is $6x - 9$. $h(x) = (6x - 9)^8$ $f(x) = x^8$ $g(x) =$ $6x - 9$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Composition" ] }

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Identify the inner and outer functions

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