Question

given f(x)=2x^2 8 and g(x)=5x-6, find each function.(f g)(x)(f*g)(x)

Answer 1

Hello,

if "*" means multiplication then

(f*g)(x)=f(x)*g(x)=g(x)*f(x)=(g*f)(x)=(2x²+8)(5x-6)=10x^3-12x²+40x-48

if "*" means composition then

(fog)(x)=f(g(x))=f(5x-6)=2*(5x-6)²+8=2(25x²-60x+36)+8=50x²-120x+80

(gof)(x)=g(f(x))=g(2x²+8)=5*(2x²+8)-6=10x²+40-6=10x²+34