The problem asks us to find $(g \circ f)(2)$, given the following functions:

$f(x) = 2x + 3$ $g(x) = 3x - 2$

The composition of functions $(g \circ f)(x)$ means that we first apply $f(x)$ and then apply $g$ to the result of $f(x)$. In mathematical terms:

$(g \circ f)(x) = g(f(x))$

Step 1: Find $f(2)$

Substitute $x = 2$ into $f(x)$:

$f(2) = 2(2) + 3 = 4 + 3 = 7$

Step 2: Find $g(f(2)) = g(7)$

Now, substitute $x = 7$ into $g(x)$:

$g(7) = 3(7) - 2 = 21 - 2 = 19$

Thus, $(g \circ f)(2) = 19$.

Answer:

The correct choice is B. $19$.

Do you have any further questions or need more details? Here are 5 related questions to expand on this concept:

1. How do you find the composition of two functions in general?
2. If $f(x) = x^2 + 1$ and $g(x) = x - 3$, what is $(g \circ f)(x)$?
3. Can you reverse the composition, i.e., find $(f \circ g)(2)$ for the given functions?
4. What is the geometric interpretation of function composition?
5. What are some applications of function composition in real-life problems?

Tip: Always be careful with the order when composing functions—$(g \circ f)(x)$ is not the same as $(f \circ g)(x)$.