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To express \( f(x) = \sqrt{x^2 + 3} \) as the composition of two functions, we need to find two functions, say \( g(x) \) and \( h(x) \), such that:

\[
f(x) = (g \circ h)(x) = g(h(x))
\]

1. **Identify the inner function** \( h(x) \) and the outer function \( g(x) \):
   - Notice that the expression inside the square root, \( x^2 + 3 \), could be represented as the inner function.
   - So, let:
     \[
     h(x) = x^2 + 3
     \]
   - Then, the square root operation is applied to \( h(x) \), so let:
     \[
     g(x) = \sqrt{x}
     \]

2. **Verify the composition**:
   - Now, if we compose \( g \) and \( h \), we get:
     \[
     g(h(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}
     \]
   - This matches \( f(x) \).

Therefore, the functions \( g(x) \) and \( h(x) \) are:
\[
g(x) = \sqrt{x} \quad \text{and} \quad h(x) = x^2 + 3
\]

### Final Answer:
\[
f(x) = g(h(x)) \quad \text{where} \quad g(x) = \sqrt{x} \quad \text{and} \quad h(x) = x^2 + 3
\]

Would you like more details or have any questions?

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Here are some related questions to deepen understanding:
1. What would the composition look like if \( f(x) = \sqrt{x + 5} \)?
2. How would you decompose \( f(x) = (x^2 + 3)^2 \) into two functions?
3. What is the purpose of decomposing functions in mathematical analysis?
4. Can you express \( f(x) = \sqrt[3]{x + 4} \) as the composition of two functions?
5. How does the order of composition (i.e., \( g(h(x)) \) vs. \( h(g(x)) \)) affect the result?

### Tip:
When decomposing functions, look for natural "layers" or "steps" in the expression, like operations inside parentheses or functions within other functions.

If f(x) = √(x² + 3), express f as the composition of two functions.

Learn how to express f(x) = √(x² + 3) as the composition of two functions. This problem covers function composition concepts and involves breaking down a square root function with a polynomial. Suitable for high school students in Grades 9-12.

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