Questions: Suppose that the functions (g) and (h) are defined as follows. [ g(x)=(x-2)(x-6) h(x)=3x-8 ] (a) Find (left(fracghright)(-5)). (b) Find all values that are NOT in the domain of (fracgh). If there is more than one value, separate them with commas. (a) (left(fracghright)(-5)=) (b) Value(s) that are NOT in the domain of (fracgh) :

Suppose that the functions (g) and (h) are defined as follows. [ g(x)=(x-2)(x-6) h(x)=3x-8 ] (a) Find (left(fracghright)(-5)). (b) Find all values that are NOT in the domain of (fracgh). If there is more than one value, separate them with commas. (a) (left(fracghright)(-5)=) (b) Value(s) that are NOT in the domain of (fracgh) :
Transcript text: Suppose that the functions $g$ and $h$ are defined as follows. \[ \begin{array}{l} g(x)=(x-2)(x-6) \\ h(x)=3 x-8 \end{array} \] (a) Find $\left(\frac{g}{h}\right)(-5)$. (b) Find all values that are NOT in the domain of $\frac{g}{h}$. If there is more than one value, separate them with commas. (a) $\left(\frac{g}{h}\right)(-5)=$ $\square$ (b) Value(s) that are NOT in the domain of $\frac{g}{h}$ : $\square$
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Solution

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Solution Steps

Step 1: Evaluating \(\left(\(frac{g}{h}\right)(a)\)

To evaluate \(\left(\(frac{g}{h}\right)(-5)\), we substitute \(x = -5\) into both \(g(x)\) and \(h(x)\). \[g(-5) = 77\] \[h(-5) = -23\] Thus, \(\left(\frac{g}{h}\right)(-5) = \frac{g)}{h} = -3.348\).

Step 2: Identifying values not in the domain

To find values of \(x\) for which \(h(x) = 0\), we solve the equation \(h(x) = 0\). The values of \(x\) that are not in the domain of \(\frac{g}{h}\) are: \(2.667\).

Final Answer:

The value of \(\left(\frac{g}{h}\right)(-5)\) is -3.348. The values not in the domain of \(\frac{g}{h}\) are: 2.667.

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