The function \( f \) is defined below. \[ f(x)=\frac{x+3}{x^{2}+12 x+27} \] Find all values of \( x \) that are NOT in the domain of \( f \). If there is more than one value, separate them with commas

To find the values of \( x \) that are not in the domain of the function \( f(x) = \frac{x+3}{x^{2}+12x+27} \), we need to identify the values of \( x \) that would make the denominator equal to zero. The denominator of the function is \( x^{2}+12x+27 \). To find the values of \( x \) that make the denominator zero, we need to solve the equation \( x^{2}+12x+27 = 0 \). Let's solve this equation to find the values of \( x \) that are not in the domain of the function \( f \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}+12x+27=0\) - step1: Factor the expression: \(\left(x+3\right)\left(x+9\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x+3=0\\&x+9=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=-3\\&x=-9\end{align}\) - step4: Rewrite: \(x_{1}=-9,x_{2}=-3\) The solutions to the equation \( x^{2}+12x+27 = 0 \) are \( x = -9 \) and \( x = -3 \). Therefore, the values of \( x \) that are not in the domain of the function \( f \) are \( x = -9 \) and \( x = -3 \). So, the values of \( x \) that are not in the domain of \( f \) are -9 and -3.