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 $g$.