Answer:
So we have
[tex](fg)(x)=3x^3+x^2-18x-6[/tex]
[tex](f \circ g)(x)=3x^2-17[/tex]
Step-by-step explanation:
I'm going to do two problems just in case.
We are given [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex].
[tex](fg)(x)=f(x)g(x)=(3x+1)(x^2-6)[/tex]
Multiply out using foil!
First: 3x(x^2)=3x^3
Outer: 3x(-6)=-18x
Inner: 1(x^2)=x^2
Last: 1(-6)=-6
-------------------Add together:
[tex]3x^3+x^2-18x-6[/tex]
[tex](f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17[/tex]
