Question

let f(x)=2x-1 and g(x)= x^2-4 find (f*g)(x)

Answer 1

Hello!

$\large\boxed{(f*g)(x)=2x^{3} - x^{2} - 8x + 4}$

To find (f · g)(x), multiply the functions f(x) and g(x):

f(x) = 2x - 1

g(x) = x² - 4

Multiply:

(2x - 1)(x² - 4)

Use the FOIL technique:

2x(x²) - 4(2x) - 1(x²) - 1(-4) =

2x³ - 8x - x² + 4

Rearrange in decreasing order of degree:

2x³ - x² - 8x + 4