https://file.aiquickdraw.com/mathbot/file/1726727800999zlr0sj6x.jpg

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.

If f(x) = √x and g(x) = x^2 + 4, then f(g(x)) is equivalent to:

Learn how to solve the function composition problem f(g(x)) where f(x) = √x and g(x) = x^2 + 4. This problem demonstrates how to combine square root and quadratic functions, including key concepts and formulas for high school math students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation