Suppose that the functions \( g \) and \( f \) are defined as follows. \[ \begin{array}{l}g(x)=x-8 \\ \text { (a) Find }\left(\frac{g}{f}\right)(-5) \text {. } \\ \text { (b) Find all values that are NOT in the domain of } \frac{g}{f} \text {. } \\ \text { If there is more than one value, separate them with commas. } \\ \text { (a) }\left(\frac{g}{f}\right)(-5)=\text { Øim } \\ \text { (b) Value(s) that are NOT in the domain of } \frac{g}{f}: \square\end{array} \]

To tackle the problems, let's break them down step by step! First, for \((\frac{g}{f})(-5)\): (a) To find \((\frac{g}{f})(-5)\), we need to know the value of \(f\) at \(-5\). As \(g(x) = x - 8\), we can find \(g(-5) = -5 - 8 = -13\). However, without \(f\), we can't proceed further. If \(f(-5) \neq 0\), then \[ \left(\frac{g}{f}\right)(-5) = \frac{g(-5)}{f(-5)} = \frac{-13}{f(-5)}. \] If \(f(-5) = 0\), then \(\left(\frac{g}{f}\right)(-5) = \text{undefined (Øim)}\). (b) The values that are NOT in the domain of \(\frac{g}{f}\) are those values for \(x\) where \(f(x) = 0\), since division by zero is undefined. Without more information about \(f(x)\), we cannot specify these values. If \(f(x)\) is a polynomial, you'd set that polynomial equal to zero and solve for \(x\). For example, if \(f(x) = x^2 - 1\), then \(x = 1, -1\) would not be in the domain. So, the answers would look like this: (a) \(\left(\frac{g}{f}\right)(-5)= \text{Øim}\) (b) Value(s) that are NOT in the domain of \(\frac{g}{f}:\) if unknown, just put \(\text{undefined}\) for the specific values.