Question

For the functions f(x)=4x⁵ and g(x)=4x²-4x, find (g°f)(x).

Answer 1

To find the composite function (g°f)(x), substitute f(x) into g(x), resulting in the composite function 64x¹⁰ - 16x⁵.

Step-by-step explanation:

To find the composite function (g°f)(x), you need to first apply the function f to x, and then apply the function g to the result of f(x). Given the functions f(x) = 4x⁵ and g(x) = 4x² - 4x, we start by computing f(x).

First, find f(x):

• f(x) = 4x⁵

Next, substitute f(x) into g(x):

• g(f(x)) = g(4x⁵) = 4(4x⁵)² - 4(4x⁵)

Simplify the expression:

• g(f(x)) = 4(16x¹⁰) - 4(4x⁵)
• g(f(x)) = 64x¹⁰ - 16x⁵

So the composite function (g°f)(x) is 64x¹⁰ - 16x⁵.