Question

For f (x) = 3x+1 and g(x) = x2 - 6, find (f.g)(x).

Answer 1

So we have

`(fg)(x)=3x^3+x^2-18x-6`

`(f \circ g)(x)=3x^2-17`

Explanation:

I'm going to do two problems just in case.

We are given
`f(x)=3x+1` and
`g(x)=x^2-6`.

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

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:

`3x^3+x^2-18x-6`

`(f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17`