Final answer:
To calculate (gof)(-2), first find f(-2) = -7, then apply it to g(x) to get g(-7) = 205. Therefore, the correct answer is (gof)(-2) = 205.
Step-by-step explanation:
To find (gof)(-2), you must first calculate f(-2) and then apply the result to g(x). Since f(x) = 3x – 1, we can substitute -2 for x to get:
f(-2) = 3(-2) – 1 = -6 – 1 = -7.
Now we will use this result as the input for g(x). With g(x) = 4x² +9, substitute -7 for x:
g(-7) = 4(-7)² + 9 = 4(49) + 9 = 196 + 9 = 205.
Therefore, (gof)(-2) = 205, which means the correct answer is b. (gof)(-2) = 205.