To solve for the opposite of [tex]\( g(x) \)[/tex], which is given by [tex]\( -g(x) \)[/tex], we will follow these steps:
1. Start with the given function [tex]\( g(x) \)[/tex].
[tex]\[ g(x) = x - 6 \][/tex]
2. To find the opposite of [tex]\( g(x) \)[/tex], multiply the entire function [tex]\( g(x) \)[/tex] by [tex]\(-1\)[/tex].
[tex]\[ -g(x) = -1 \cdot (x - 6) \][/tex]
3. Distribute the [tex]\(-1\)[/tex] across the terms inside the parentheses.
[tex]\[ -g(x) = -x + 6 \][/tex]
So, the opposite of [tex]\( g(x) \)[/tex] is:
[tex]\[ -g(x) = -x + 6 \][/tex]
Thus, [tex]\( -g(x) = -x + 6 \)[/tex] is the solution.
