Question

what is $f(x) + f(x) + f(x)$?
complete
$3f(x) = $
complete
evaluate $3f(2) = 12$
complete
$g(x) = x - 6$
if the opposite of $g(x)$ is $-g(x)$, then $-g(x) = $
done
options: $-x - 6$, $-x + 6$, $x + 6$

Explanation:

Step1: Recall the definition of the opposite of a function

To find \(-g(x)\) when \(g(x)=x - 6\), we need to apply the negative sign to the entire function \(g(x)\).

Step2: Apply the negative sign to \(g(x)\)

Using the distributive property of multiplication over addition (or subtraction), we have \(-g(x)=-(x - 6)\).
Expanding the right - hand side, we get \(-g(x)=-x+6\) (because \(-(a - b)=-a + b\), here \(a = x\) and \(b = 6\)).

Answer:

\(-x + 6\) (corresponding to the option \(-x+6\))