Certainly! Let's solve the given expression step by step.
We start with the expression:
[tex]\[ g(x) + (-g(x)) \][/tex]
1. Identify the components in the expression:
- [tex]\( g(x) \)[/tex] is a function.
- [tex]\( -g(x) \)[/tex] is the negative of the function [tex]\( g(x) \)[/tex].
2. Add the components together:
- When you add [tex]\( g(x) \)[/tex] and [tex]\( -g(x) \)[/tex], you are essentially adding a function and its negative.
3. Simplify the expression:
- Adding a function and its negative will always result in zero. Mathematically, it looks like this:
[tex]\[
g(x) + (-g(x)) = 0
\][/tex]
So, the simplified result of the expression is:
[tex]\[\boxed{0}\][/tex]
Therefore, the correct option from the list provided is:
[tex]\[ 0 \][/tex]
