Final answer:
To find (fog)(3), we first need to find the value of g(3) and then substitute that value into f(x). By substituting x = 3 into the expression for g(x), we find that g(3) = 45. Substituting g(3) into f(x), we find that (fog)(3) = 134. Thus, (fog)(3) = 134, which corresponds to option D.
Step-by-step explanation:
To find (fog)(3), we first need to find the value of g(3) and then substitute that value into f(x).
To find g(3), we substitute x = 3 into the expression for g(x):
g(3) = 4(3)² + 9 = 4(9) + 9 = 36 + 9 = 45
Now, we can substitute g(3) into f(x) to find (fog)(3):
f(g(3)) = f(45) = 3(45) - 1 = 135 - 1 = 134
Therefore, (fog)(3) = 134, so the correct answer is D. (fog)(3) = 134.
To find (fog)(3), we need to first evaluate g(3) and then apply the function f to that result. Here's how it works step by step:
First find g(3): g(x) = 4x² + 9, so g(3) = 4(3)² + 9 = 4(9) + 9 = 36 + 9 = 45.
Now apply f to g(3): f(x) = 3x - 1, so f(g(3)) = f(45) = 3(45) - 1 = 135 - 1 = 134.
Thus, (fog)(3) = 134, which corresponds to option D.