Questions: Suppose that the functions g and f are defined as follows. g(x)=x-1 f(x)=(x+3)(x+1) (a) Find (g/f)(-6) (b) Find all values that are NOT in the domain of g/f. If there is more than one value, separate them with commas. (a) (g/f)(-6)= (b) Value(s) that are NOT in the domain of g/f :

Suppose that the functions g and f are defined as follows.

g(x)=x-1
f(x)=(x+3)(x+1)

(a) Find (g/f)(-6)
(b) Find all values that are NOT in the domain of g/f.

If there is more than one value, separate them with commas.
(a) (g/f)(-6)=
(b) Value(s) that are NOT in the domain of g/f :

Transcript text: Suppose that the functions $g$ and $f$ are defined as follows. \[ \begin{array}{l} g(x)=x-1 \\ f(x)=(x+3)(x+1) \end{array} \] (a) Find $\left(\frac{g}{f}\right)(-6)$ (b) Find all values that are NOT in the domain of $\frac{g}{f}$. If there is more than one value, separate them with commas. (a) $\left(\frac{g}{f}\right)(-6)=$ $\square$ (b) Value(s) that are NOT in the domain of $\frac{g}{f}$ : $\square$

Solution

Solution Steps

Step 1: Evaluate the Quotient at a Specific Point $x_0$

To find $\left(\frac{f}{g}\right)(x_0)$, substitute $x_0 = -6$ into both $f(x)$ and $g(x)$ and compute the quotient. Given $f(x) = x - 1$ and $g(x) = (x + 1)*(x + 3)$, $f(-6) = -7$ and $g(-6) = 15$. Thus, $\left(\frac{f}{g}\right)(-6) = -0.467$.

Step 2: Determine the Domain of \(

rac{f}{g}\) To find all values not in the domain of $ rac{f}{g}$, solve the equation $g(x) = 0$. The values of $x$ for which $g(x) = 0$ are [-3, -1], which are excluded from the domain of $ rac<function g at 0xffff7821fa30><function f at 0xffff7821f010>$.

Final Answer:

The quotient $\left(\frac{f}{g}\right)(-6)$ is -0.467, and the values excluded from the domain of $ rac<function g at 0xffff7821fa30><function f at 0xffff7821f010>$ are [-3, -1].

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