If f(x)=x^3-3-2xf(x)=x332x, and g(x)=x-1g(x)=x1, what is (f*g)(x)(fg)(x)?

2 Answers
Jun 18, 2018

x^3-3*x^2+x-2x33x2+x2

Explanation:

(f*g)(x)=f(g(x))(fg)(x)=f(g(x))
f(g(x))=(x-1)^3-2(x-1)-3f(g(x))=(x1)32(x1)3
=x^3-3*x^2+x-2=x33x2+x2

Jun 18, 2018

x^4-x^3-2x^2-x+3x4x32x2x+3

Explanation:

(f*g)(x)=f(x)xxg(x)(fg)(x)=f(x)×g(x)

=(x^3-3-2x)(x-1)=(x332x)(x1)

=color(red)(x^3)(x-1)color(red)(-3)(x-1)color(red)(-2x)(x-1)=x3(x1)3(x1)2x(x1)

=x^4-x^3color(blue)(-3x)+3-2x^2color(blue)(+2x)=x4x33x+32x2+2x

=x^4-x^3-2x^2-x+3=x4x32x2x+3