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+?+(?)√x+3

Answer 1

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

Given:

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

Now, multiplying \(f(x)\) and \(g(x)\):

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

Using the distributive property (FOIL method):

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

Now calculate each term:

1. The first term:
\[
\sqrt{x + 3} \cdot \sqrt{x + 3} = x + 3
\]

2. The second term:
\[
-2 \cdot \sqrt{x + 3} = -2\sqrt{x + 3}
\]

Putting it all together:

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

So, we can express this as:

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

To put it in the required format \(x + ? + (?)\sqrt{x + 3}\):

1. The first missing value is \(3\).
2. The second missing value is \(-2\).

Thus,

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

The final answer is:

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

The missing values are \(3\) and \(-2\).