Let $f(x) = 3x + 4$ and $g(x) = x^2 + x\text{.}$ Find the composite functions $(f \circ g)$ and $(g \circ f)$ by using $x$ as the input. Remember to simplify the expression inside the parentheses first.

1. $f(g(x))\text{.}$ We can first substitute the expression for $g(x)$ inside the parentheses, and then use that expression as the input for $f\text{.}$
   $$\begin{aligned} f(g(x)) \amp= f\mathopen{}\left(x^2 + x\right)\mathclose{}\\ \amp= 3\left(x^2 + x\right) + 4\\ \amp= 3x^2 + 3x + 4 \end{aligned}$$
2. $g(f(x))\text{.}$ We can first substitute the expression for $f(x)$ inside the parentheses, and then use that expression as the input for $g\text{.}$
   $$\begin{aligned} g(f(x)) \amp= g(3x + 4)\\ \amp= (3x + 4)^2 + (3x + 4)\\ \amp= 9x^2 + 24x + 16 + 3x + 4\\ \amp= 9x^2 + 27x + 20 \end{aligned}$$

So we found:

1. $f(g(x))=$
2. $g(f(x))=$