Question

Let f(x)=2x^(2)-4x+2 and g(x)=x-1. Perform the funct (f o g)(x)

Answer 1

To perform the function composition (f o g)(x), substitute the function g(x) into f(x). The final answer is f(g(x)) = 2x^2 - 8x + 8.

Step-by-step explanation:

To perform the function composition (f o g)(x), we substitute the function g(x) into f(x).

First, find g(x): g(x) = x - 1

Then, substitute g(x) into f(x): f(g(x)) = f(x - 1)

Simplify f(g(x)): f(g(x)) = 2(x - 1)^2 - 4(x - 1) + 2

Now, expand and simplify: f(g(x)) = 2(x^2 - 2x + 1) - 4x + 4 + 2

Combine like terms: f(g(x)) = 2x^2 - 4x + 2 - 4x + 4 + 2

Final answer: f(g(x)) = 2x^2 - 8x + 8