Quotient of two functions: Basic
Suppose that the functions $g$ and $f$ are defined as follows.
\[
\begin{array}{l}
g(x)=5-3 x^{2} \\
f(x)=8-3 x
\end{array}
\]
(a) Find $\left(\frac{g}{f}\right)(-1)$.
(b) Find all valies that are NOT in the domain of $\frac{g}{f}$. If there is more than one value, separate them with commas.
Answer
Final Answer for part (b): Value(s) that are NOT in the domain of \(\frac{g}{f}\) : \(\boxed{\frac{8}{3}}\)
Step 1 ：First, we need to find the value of \(\left(\frac{g}{f}\right)(-1)\). This is done by substituting \(x=-1\) into the function \(\frac{g(x)}{f(x)}\).
Step 2 ：Next, we need to find the values that are not in the domain of \(\frac{g}{f}\). These are the values of \(x\) for which \(f(x) = 0\), because division by zero is undefined in mathematics. So we solve the equation \(f(x) = 0\) to find these values.
Step 3 ：Final Answer for part (a): \(\left(\frac{g}{f}\right)(-1) = \boxed{-1.0}\)
Step 4 ：Final Answer for part (b): Value(s) that are NOT in the domain of \(\frac{g}{f}\) : \(\boxed{\frac{8}{3}}\)
