Question 35.
Given:
[tex]\begin{gathered} f(x)=x-5 \\ \\ g(x)=\sqrt[]{x+3} \\ \\ \text{Let's solve for }\frac{f(x)}{g(x)} \end{gathered}[/tex]
To solve the function operation, let's divide both functions.
Hence, we have:
[tex]\frac{f(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}}[/tex]
Now, let's find the domain of the function f(x)/g(x).
Domain is the set of all possible x-values that makes the function true.
Hence, to find the domain, set the expression in the radicand equal to zero.
We have:
x + 3 = 0
Subtract 3 fromboth sides:
x + 3 - 3 = 0 - 3
x = - 3
Therefore, the domain in interval notation is:
(-3, ∞).
ANSWER:
[tex]\begin{gathered} \frac{h(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}} \\ \\ \text{Domain:}(-3,\infty) \end{gathered}[/tex]
