Final answer:
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.