Question

g(x) = x - 6
if the opposite of g(x) is -g(x),
then -g(x) =
done

Explanation:

Step1: Identify the function

We have the function \( g(x) = x - 6 \).

Step2: Find the opposite of \( g(x) \)

To find \( -g(x) \), we multiply the entire function \( g(x) \) by -1. So, \( -g(x)=-(x - 6) \).

Step3: Distribute the negative sign

Using the distributive property \( - (a - b)=-a + b \), we get \( -g(x)=-x + 6 \).

Answer:

\( -x + 6 \) (or equivalently \( 6 - x \))