Questions: f(x)=3x-3 g(x)=x^2-9x+8 Find (f/g)(x) (f/g)(x)= The domain of (f/g)(x) is x ≠

Transcript text: \[ \begin{array}{l} f(x)=3 x-3 \\ g(x)=x^{2}-9 x+8 \\ \text { Find }\left(\frac{f}{g}\right)(x) \\ \left(\frac{f}{g}\right)(x)=\square \end{array} \] The domain of $\left(\frac{f}{g}\right)(x)$ is $x \neq$ $\square$

Solution

Solution Steps

Step 1: Simplify the Quotient

To simplify the quotient $\left(\frac{f}{g}\right)(x)$, we divide $f(x)$ by $g(x)$. Given $f(x) = 3 x - 3$ and $g(x) = x^{2} - 9 x + 8$, the simplified form is $\frac{3}{x - 8}$.

Step 2: Determine the Domain

The domain of $\left(\frac{f}{g}\right)(x)$ consists of all real numbers except those that make $g(x) = 0$. To find these values, we solve $g(x) = 0$ and find the roots: $\left\{1, 8\right\}$. These values are excluded from the domain, so the domain of the quotient function is $\left(-\infty, 1\right) \cup \left(1, 8\right) \cup \left(8, \infty\right)$.

Final Answer:

The simplified form of the quotient is $\frac{3}{x - 8}$, rounded to 2 decimal places if necessary. The domain of the quotient function, excluding points where $g(x) = 0$, is $\left(-\infty, 1\right) \cup \left(1, 8\right) \cup \left(8, \infty\right)$.

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