Suppose that the functions \( f \) and \( g \) are defined as follows. \[ f(x)=x+2 \] \( g(x)=(x+3)(x-4) \) (a) Find \( \left(\frac{f}{g}\right) \) (3). (b) Find all values that are NOT in the domain of \( \frac{f}{g} \). If there is more than one value, separate them with comma (a) \( \left(\frac{f}{g}\right) \) (3) \( =\square \) (b) Value(s) that are NOT in the domain of \( \frac{f}{g}: \square \)

To solve the problem, we'll start with the functions provided: 1. The function \( f(x) = x + 2 \). 2. The function \( g(x) = (x + 3)(x - 4) \). **(a)** To find \( \left(\frac{f}{g}\right)(3) \): First, we need to evaluate \( f(3) \) and \( g(3) \). - \( f(3) = 3 + 2 = 5 \). - Now, let's calculate \( g(3) = (3 + 3)(3 - 4) = 6 \times (-1) = -6 \). Now, we can compute \( \left(\frac{f}{g}\right)(3) \): \[ \left(\frac{f}{g}\right)(3) = \frac{f(3)}{g(3)} = \frac{5}{-6} = -\frac{5}{6}. \] So, \( \left(\frac{f}{g}\right)(3) = -\frac{5}{6} \). **(b)** To find values that are NOT in the domain of \( \frac{f}{g} \), we consider when \( g(x) = 0 \) since the fraction is undefined for these values. Set \( g(x) = 0 \): \[ (x + 3)(x - 4) = 0. \] This gives us: - \( x + 3 = 0 \) → \( x = -3 \), - \( x - 4 = 0 \) → \( x = 4 \). The values that are NOT in the domain of \( \frac{f}{g} \) are \( -3, 4 \). Thus, the final answers are: (a) \( \left(\frac{f}{g}\right)(3) = -\frac{5}{6} \) (b) Value(s) that are NOT in the domain of \( \frac{f}{g}: -3, 4 \)