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.