To find \( (f + g)(x) \) when you have two functions \( f(x) \) and \( g(x) \), you simply add the two functions together.

Given the functions:

\[
f(x) = \sqrt{x^2 - 4}
\]

\[
g(x) = \frac{x^2}{x^2 + 1}
\]

The function \( (f + g)(x) \) is:

\[
(f + g)(x) = \sqrt{x^2 - 4} + \frac{x^2}{x^2 + 1}
\]

This is the simplified form of \( (f + g)(x) \).

Would you like to explore any details or have any further questions?

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Here are 5 related questions you might be interested in:

1. What is the domain of the function \( f(x) = \sqrt{x^2 - 4} \)?
2. How do you simplify \( \sqrt{x^2 - 4} \)?
3. What are the critical points of \( g(x) = \frac{x^2}{x^2 + 1} \)?
4. How do you find the derivative of \( (f + g)(x) \)?
5. What are the asymptotes of \( g(x) = \frac{x^2}{x^2 + 1} \)?

**Tip:** When adding two functions, ensure you consider their individual domains to find the domain of the resulting function.

Learn how to find the sum of functions (f + g)(x) where f(x) = √(x^2 - 4) and g(x) = x^2/(x^2 + 1). This problem involves key concepts in algebra, including radicals and rational functions, and is suitable for students in Grades 9-12.

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