The problem is asking for the value of $(g \circ f)(2)$, where the functions $f(x)$ and $g(x)$ are defined as follows:

• $f(x) = 2x^2 + 5x - 7$
• $g(x) = 3x - 12$

To solve for $(g \circ f)(2)$, which is the composition of functions, we proceed with the following steps:

Step 1: Calculate $f(2)$

Substitute $x = 2$ into the function $f(x)$: $f(2) = 2(2)^2 + 5(2) - 7$ $f(2) = 2(4) + 10 - 7 = 8 + 10 - 7 = 11$

Step 2: Calculate $g(f(2)) = g(11)$

Now, substitute $f(2) = 11$ into the function $g(x)$: $g(11) = 3(11) - 12$ $g(11) = 33 - 12 = 21$

Thus, $(g \circ f)(2) = 21$.

The correct answer is B. 21.

Would you like further details on any steps? Here are five related questions for practice:

1. What is $(f \circ g)(2)$?
2. How do you find the domain of a composite function?
3. If $g(x) = x^3 - 1$, what is $(g \circ f)(2)$ for the same $f(x)$?
4. How would the answer change if $f(x)$ were a linear function?
5. How can you verify the result of a composite function graphically?

Tip: When dealing with composite functions, always evaluate the inner function first and then apply the result to the outer function.