Problem

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

Solution

Step 1 :For part (a), we need to find the value of \(\left(\frac{h}{g}\right)(2)\). This means we need to substitute \(x=2\) into the function \(\frac{h(x)}{g(x)}\).

Step 2 :For part (b), the values that are not in the domain of \(\frac{h}{g}\) are the values of \(x\) for which \(g(x) = 0\), because division by zero is undefined in mathematics. So we need to solve the equation \(g(x) = 0\) to find these values.

Step 3 :Final Answer: (a) \(\left(\frac{h}{g}\right)(2) = \boxed{-9.0}\)

Step 4 :Final Answer: (b) Value(s) that are NOT in the domain of \(\frac{h}{g}\) : \(\boxed{3}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7724/

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