Theirsum, denoted by f+g, is the function denoted by (f+g)(x)=f(x)+g(x)

Yes, that's correct!

The sum of two functions \( f \) and \( g \), denoted by \( (f+g)(x) \), is defined as:

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

This means that to find the value of the new function \( (f+g)(x) \) at any point \( x \), you simply add the values of \( f(x) \) and \( g(x) \) together.

If you have two functions:
- \( f(x) \), and
- \( g(x) \),

Their sum is another function that for each input \( x \) returns the sum of the outputs of \( f(x) \) and \( g(x) \).

Would you like more details or have any questions about function operations? 

Here are 5 related questions:
1. How do you find the difference of two functions \( (f - g)(x) \)?
2. What happens if one of the functions is a constant, such as \( f(x) = 3 \)?
3. Can you multiply two functions together, and how is that defined?
4. What is the result if \( f(x) = x^2 \) and \( g(x) = x + 1 \)?
5. How would the sum of two functions work if both are piecewise functions?

**Tip**: When adding functions, the domain of the resulting function \( f+g \) is the intersection of the domains of \( f \) and \( g \).

Their sum, denoted by f+g, is the function denoted by (f+g)(x)=f(x)+g(x)

Learn how to add two functions, f and g, with a detailed explanation of the formula (f+g)(x) = f(x) + g(x). This algebra problem covers the basics of function addition, making it suitable for high school students in Grades 9-12.

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