Question

g(x) = x - 6
if the opposite of g(x) is -g(x),
then -g(x) =
complete
g(x) + (-g(x)) =
done
options: 2g(x), -2g(x), 0

Explanation:

Step1: Recall the property of opposite

The opposite of a function \( g(x) \) is \( -g(x) \), and we know that for any number (or function) \( a \) and its opposite \( -a \), \( a+(-a)=0 \).

Step2: Apply the property to \( g(x) \) and \( -g(x) \)

Substitute \( a = g(x) \) into the formula \( a+(-a) \), we get \( g(x)+(-g(x))=g(x)-g(x) \).
Since \( g(x)-g(x) = 0 \) (subtracting a function from itself gives zero), so \( g(x)+(-g(x)) = 0 \).

Answer:

\( 0 \)