Please I need some help

Question

Given that f(x)=−3x^2+2x and g(x)=2x−1, determine each of the following. Make sure to fully simplify your answer.

(a) (f∘g)(x)=   

(b) (g∘f)(x)=   

(c) (f∘f)(x)=

   

(d) (g∘g)(x)= 

Answer 1

f(x)= -3x^2 +2x

g(x) = 2x-1

f(g(x))= f(2x-1) = -3(2x-1)^2 + 2(2x-1) = -3(4x^2-4x+1)+4x-2

=-12x^2+12x-3+4x-2

=-12x^2+16x-5

g(f(x)) = g(-3x^2+2x)= 2(-3x^2+2x) -1 = -6x^2+4x-1

f(f(x)) = f(-3x^2+2x) =-3(-3x^2+2x)^2 +2(-3x^2+2x)

= -3(9x^4-12x^3+4x^2) -6x^2 +4x

=-27x^4+36x^3 -12^2-6x^2+4x

=-27x^4 +36x^3-18x^2 +4x

g(g(x)) = g(2x-1) = 2(2x-1)-1 = 4x-2-1=4x-3