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

To find \((f \circ g)(x)\), we need to substitute \(g(x)\) into \(f(x)\). 1. First, we compute \(g(x)\): \[ g(x) = 3x^2 - 6x - 6. \] 2. Next, substitute \(g(x)\) into \(f(x)\): \[ f(g(x)) = f(3x^2 - 6x - 6). \] Since \(f(x) = -3x + 12\), we replace \(x\) with \(3x^2 - 6x - 6\): \[ f(g(x)) = -3(3x^2 - 6x - 6) + 12. \] 3. Now simplify this expression: \[ = -9x^2 + 18x + 18 + 12, \] \[ = -9x^2 + 18x + 30. \] 4. Finally, write the polynomial in standard form: \[ (f \circ g)(x) = -9x^2 + 18x + 30. \] So, the answer is: \[ (f \circ g)(x) = -9x^2 + 18x + 30. \]