In mathematics, the notation \((f + g)(x)\) refers to the sum of two functions \(f(x)\) and \(g(x)\) applied to the same input \(x\). The equation you provided:

\[
(f + g)(x) = f(x) + g(x)
\]

means that the result of adding the two functions first (i.e., \(f(x) + g(x)\)) is the same as first adding the two functions as a whole, and then applying the input \(x\). This is a standard property of function addition.

Here's a breakdown:
- \((f + g)(x)\) is the notation for the function that results from adding the functions \(f\) and \(g\), and then evaluating at \(x\).
- \(f(x) + g(x)\) means we are evaluating \(f(x)\) and \(g(x)\) separately at the input \(x\), and then adding the two results.

This property is true for all functions where the sum of the functions is well-defined at each input \(x\).

Would you like more detailed examples or clarifications on this? Here are a few related questions you can explore:

1. What happens when you multiply two functions, \((f \cdot g)(x)\)?
2. Can you subtract functions in a similar way?
3. How do you handle composite functions, like \((f \circ g)(x)\)?
4. What are some common applications of function addition?
5. How does function addition work with trigonometric or exponential functions?

**Tip:** When working with functions, always keep in mind the domain where both functions are defined to avoid errors in evaluation.

Explore how function addition works through the equation (f + g)(x) = f(x) + g(x). This guide breaks down key concepts in algebra and functions, explaining how to sum two functions and evaluate them at the same input. Ideal for high school students in Grades 10-12.

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