Final answer:
The composition of the functions g(x) and h(x), denoted by (g°h)(x), is found by substituting h(x) into g(x), leading to (g°h)(x) = -3x² + 20x - 32.
Step-by-step explanation:
To find (g°h)(x), we first need to understand that this notation represents the composition of the functions g and h, meaning we need to evaluate the function g at the values provided by h(x). Given g(x) = -3x² + 4x and h(x) = -x + 4, we substitute h(x) into g(x) to calculate g(h(x)).
First, evaluate h(x): h(x) = -x + 4.
Next, substitute h(x) into g(x):
g(h(x)) = g(-x + 4) = -3(-x + 4)² + 4(-x + 4).
Expand and simplify:
g(h(x)) = -3(x² - 8x + 16) - 4x + 16
g(h(x)) = -3x² + 24x - 48 - 4x + 16
g(h(x)) = -3x² + 20x - 32.
Therefore, the composition (g°h)(x) is -3x² + 20x - 32.