Problem

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.

Solution

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 \(\frac{g}{f}\) : \(\boxed{\frac{8}{3}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/rmd0I29bpE/

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