QuestionConsider the functions $g(x)$ and $f(x)$, and evaluate the expressions below: $$\begin{array}{l} g(x)=3 x+6 \\ f(x)=-4 x-6 \\ g(2)=\square \\ f(2)=\square \\ g(f(x))=\square \\ g(f(2))=\square \end{array}$$

Studdy Solution
To evaluate $g(f(2))$, first find $f(2)$ which we calculated as $-14$, then substitute into $g(x) = 3x + 6$:
$$g(f(2)) = g(-14) = 3(-14) + 6$$
Calculate:
$$g(f(2)) = -42 + 6 = -36$$
The evaluated expressions are: - $g(2) = 12$ - $f(2) = -14$ - $g(f(x)) = -12x - 12$ - $g(f(2)) = -36$