Question

Use the functions below.

f(x)=x+3−−−−√−2

g(x)=x+3−−−−√

What is (f⋅g)(x)
?

Enter the missing values.

(1 point)
(f⋅g)(x)=x+
$$

Answer 1

To find \((f \cdot g)(x)\), we need to multiply the two functions \(f(x)\) and \(g(x)\).

Given:
- \(f(x) = \sqrt{x + 3} - 2\)
- \(g(x) = \sqrt{x + 3}\)

Now, let's multiply these two functions:

\[
(f \cdot g)(x) = f(x) \cdot g(x) = (\sqrt{x + 3} - 2) \cdot \sqrt{x + 3}
\]

Next, we can use the distributive property to expand this multiplication:

\[
(f \cdot g)(x) = \sqrt{x + 3} \cdot \sqrt{x + 3} - 2 \cdot \sqrt{x + 3}
\]

This simplifies to:

\[
(f \cdot g)(x) = (x + 3) - 2\sqrt{x + 3}
\]

Thus, we can express this as:

\[
(f \cdot g)(x) = x + 3 - 2\sqrt{x + 3}
\]

Therefore, the final answer is:

\[
\boxed{x + 3 - 2\sqrt{x + 3}}
\]

If we need to fill in the specific parts as you mentioned, we should note:
- The answer for your completion is \(x + 3\), while the missing part regarding \(g(x)\) would be the term \(- 2\sqrt{x + 3}\).