To solve the problem and find [tex]\((f \circ g)(-3)\)[/tex], let's break it down step by step.
Firstly, let's understand what [tex]\((f \circ g)(x)\)[/tex] means. This notation is read as "f of g of x," which means we need to first apply the function [tex]\(g(x)\)[/tex] and then apply the function [tex]\(f\)[/tex] to the result obtained from [tex]\(g(x)\)[/tex].
We have the functions:
[tex]\[ g(x) = x^3 \][/tex]
[tex]\[ f(x) = 2x \][/tex]
Step 1: Evaluate [tex]\(g(-3)\)[/tex]
[tex]\[ g(-3) = (-3)^3 = -27 \][/tex]
Step 2: Use the result from Step 1 as the input for the function [tex]\(f\)[/tex]:
[tex]\[ f(g(-3)) = f(-27) \][/tex]
Step 3: Evaluate [tex]\(f(-27)\)[/tex]
[tex]\[ f(-27) = 2 \times -27 = -54 \][/tex]
Therefore, [tex]\((f \circ g)(-3) = -54\)[/tex].
The correct answer is:
D. -54
