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Suppose that the functions $h$ and $g$ are defined as follows.
\[
\begin{array}{l}
h(x)=x+6 \\
g(x)=(x-4)(x-2)
\end{array}
\]
(a) Find $\left(\frac{h}{g}\right)(5)$.
(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) $\left(\frac{6}{3}\right)(5)=0$
Answer
Final Answer: (b) Value(s) that are NOT in the domain of \(\frac{h}{g}\) : \(\boxed{2,4}\)
Step 1 ：For part (a), we need to find the value of \(\left(\frac{h}{g}\right)(5)\). This means we need to substitute \(x=5\) 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) \(\left(\frac{h}{g}\right)(5) = \boxed{0.5}\)
Step 4 ：Final Answer: (b) Value(s) that are NOT in the domain of \(\frac{h}{g}\) : \(\boxed{2,4}\)
