The function \( f \) is defined below. \[ f(x)=\frac{x+3}{x^{2}+7 x+12} \] 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 determine the values of \( x \) that are not in the domain of the function \( f(x) = \frac{x+3}{x^2 + 7x + 12} \), we need to find the points where the denominator is equal to zero, as division by zero is undefined. First, we can factor the quadratic in the denominator: \[ x^2 + 7x + 12 = (x + 3)(x + 4) \] Now, we set the denominator equal to zero: \[ (x + 3)(x + 4) = 0 \] This gives us two solutions: 1. \( x + 3 = 0 \) which leads to \( x = -3 \) 2. \( x + 4 = 0 \) which leads to \( x = -4 \) Thus, the values of \( x \) that are NOT in the domain of \( f \) are: \[ \boxed{-3, -4} \]