Question

Let f(x) = x^(2) - x and g(x) = 2x + 1. Find and simplify the following. (g*f)(x)

Answer 1

To find (g*f)(x), substitute the function g(x) = 2x + 1 into the function f(x) = x^2 - x. Expanding and simplifying, we get (g*f)(x) = 4x^2 + 2x.

Step-by-step explanation:

To find (g*f)(x), we need to substitute the function g(x) = 2x + 1 into the function f(x) = x^2 - x.

Substituting g(x) into f(x), we get:

(g*f)(x) = f(g(x)) = f(2x + 1) = (2x + 1)^2 - (2x + 1).

Expanding and simplifying, we have:

(g*f)(x) = 4x^2 + 4x + 1 - 2x - 1 = 4x^2 + 2x.