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

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

Step-by-step 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