Question

Question 35?Find the indicated function and state its domain in interval notation?

Answer 1

Question 35.

Given:

`\begin{gathered} f(x)=x-5 \\ \\ g(x)=\sqrt[]{x+3} \\ \\ \text{Let's solve for }(f(x))/(g(x)) \end{gathered}`

To solve the function operation, let's divide both functions.

Hence, we have:

`(f(x))/(g(x))=\frac{x-5}{\sqrt[]{x+3}}`

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:

`\begin{gathered} (h(x))/(g(x))=\frac{x-5}{\sqrt[]{x+3}} \\ \\ \text{Domain:}(-3,\infty) \end{gathered}`