The expression \((f + g)(x)\) represents the sum of two functions \(f(x)\) and \(g(x)\). Specifically, it's defined as:

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

This means you add the outputs of \(f(x)\) and \(g(x)\) for a given value of \(x\). If you have explicit forms of \(f(x)\) and \(g(x)\), you can directly add them together.

Would you like to provide the functions \(f(x)\) and \(g(x)\) for a more detailed solution?

Here are 5 related questions that you might find useful:
1. What happens if \(f(x)\) or \(g(x)\) are polynomials?
2. How does the operation change if \(f(x)\) and \(g(x)\) are trigonometric functions?
3. Can \(f(x)\) and \(g(x)\) be defined piecewise? How would their sum behave then?
4. What is the domain of the function \((f+g)(x)\)?
5. How does this operation differ from function multiplication, \((f \cdot g)(x)\)?

**Tip:** When adding functions, make sure to consider their domains, as the domain of \((f + g)(x)\) will be the intersection of the domains of \(f(x)\) and \(g(x)\).

Understand how to add two functions with the expression (f + g)(x), which represents the sum of the outputs of f(x) and g(x) for any given value of x. This guide includes the core concept of function addition, detailed explanations, and related questions to explore. Suitable for students in Grades 9-12.

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