The problem is asking for $f(g(x))$, where:

• $f(x) = \sqrt{x}$
• $g(x) = x^2 + 4$

Step-by-step solution:

1. Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(x^2 + 4)$ Since $f(x) = \sqrt{x}$, replace the input in $f$ with $g(x) = x^2 + 4$:

   $f(g(x)) = \sqrt{x^2 + 4}$

Conclusion:

The correct answer is $\sqrt{x^2 + 4}$, which matches the fourth option: $\boxed{\sqrt{x^2 + 4}}$

Would you like more details on any specific step?

Here are five related questions to further your understanding:

1. What is the composition of functions and how is it applied here?
2. How does the domain of $f(g(x))$ change based on the functions $f(x)$ and $g(x)$?
3. What happens if we reverse the functions, i.e., compute $g(f(x))$?
4. Can the expression $\sqrt{x^2 + 4}$ be simplified further?
5. How would the result change if the function $g(x)$ were different, e.g., $g(x) = x^2 - 4$?

Tip: When composing functions, always ensure you're substituting the entire function, not just part of it.