Final answer:
To find (g*f)(x), substitute f(x) into g(x) and simplify.
Step-by-step explanation:
To find (g*f)(x), we need to perform the operation of composition of functions. This means that we will substitute f(x) into g(x) and simplify.
g(x) = -x² + 5x
f(x) = 4x + 1
(g*f)(x) = g(f(x))
Substituting f(x) into g(x):
(g*f)(x) = -(4x + 1)² + 5(4x + 1)
(g*f)(x) = -(16x² + 8x + 1) + 20x + 5
(g*f)(x) = -16x² + 12x + 4