Express your answer as a polynomial in standard form. $$ \begin{array}{l}f(x)=-3 x+12 \ g(x)=3 x^{2}-6 x-6 \ \text { Find: }(f \circ g)(x)\end{array} $$ Answer Attempt out of 2

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To find the composition of functions $$ f \circ g $$, we need to substitute the expression for $$ g(x) $$ into $$ f(x) $$ and simplify.

Given:
$$ f(x) = -3x + 12 $$
$$ g(x) = 3x^2 - 6x - 6 $$

Substitute $$ g(x) $$ into $$ f(x) $$:
$$ (f \circ g)(x) = f(g(x)) = -3(g(x)) + 12 $$

Substitute the expression for $$ g(x) $$ into the equation:
$$ (f \circ g)(x) = -3(3x^2 - 6x - 6) + 12 $$

Simplify the expression:
$$ (f \circ g)(x) = -9x^2 + 18x + 18 + 12 $$
$$ (f \circ g)(x) = -9x^2 + 18x + 30 $$

Therefore, the composition of functions $$ f \circ g $$ is $$ -9x^2 + 18x + 30 $$.
$$ (f \circ g)(x) = -9x^2 + 18x + 30 $$

Express your answer as a polynomial in standard form.

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Express your answer as a polynomial in standard form. Answer Attempt out of 2