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 \(- 2\sqrt{x + 3}\).