Final answer:
To find (g o f) (-3x), substitute -3x into both functions and simplify the resulting composed function.
Step-by-step explanation:
To find (g o f) (-3x), we need to substitute the given function values into the composed function equation. First, we find f(-3x) by replacing t in f(t) = t + 1 with -3x:
f(-3x) = (-3x) + 1 = -3x + 1.
Next, we find g(f(-3x)) by replacing t in g(t) = t³ - 12t² + 2x with -3x + 1:
g(f(-3x)) = (-3x + 1)³ - 12(-3x + 1)² + 2x.
Simplifying this expression further will give us the final answer.