Question

For the functions f(x)=−x2+2x−1 and g(x)=x−1, find (fg)(x) and (fg)(0).

Answer 1

The answer to your question is (fg)(x) = x² - 2; (fg)(0) = -2

Explanation:

Data

f(x) = x² + 2x - 1

g(x) = x - 1

(fg)(x) = ?

(fg)(0) = ?

Process

1.- Evaluate f(x) in g(x)

f(g)(x) = (x -1)² + 2(x - 1) - 1

- Simplify

(fg)(x) = x² - 2x + 1 + 2x - 2 - 1

(fg)(x) = x² - 2

2.- Evaluate (fg)(x) when x = 0

(fg)(0) = (0)² - 2

- Simplify

(fg)(0) = 0 - 2

(fg)(0) = -2