Given the functions, f(x) = x - 8 and g(x) = x2 + x - 1, perform the indicated operation. when applicable, state the domain restriction.
(fg)(x).
1. x3 - 7x2 - 9x + 8
2. x3 - 9x2 - 9x + 8
3. x3 - 9x2 - 9x - 8
4. x3 - 7x2 - 9x - 8

(fg)(x)= x^3 -7x^2 -9x +8

domain is (-∞,∞)

Step-by-step explanation:

f(x)= x-8

g(x)= x^2 +1x -1

To find (fg)(x) we multiply f(x) and g(x)

(fg)(x) = f(x) * g(x)

(fg)(x)= (x-8) (x^2+x-1)

Multiply x with x^2 +x-1

x^3 +x^2 - x

multiply -8 with x^2 +x -1

-8x^2 -8x+8

(fg)(x)= (x-8) (x^2+x-1)

(fg)(x)= x^3 + x^2 -x -8x^2 -8x +8

combine like terms

(fg)(x)= x^3 -7x^2 -9x +8

Domain of all cubic function is set of all real numbers

domain is (-∞,∞)