Let F(X)=4x+3 and G(X)=2x^2 +4x

Question

After Simplifying

(F * G) (X)=

I was first wanting to put them into parentheses next to each other because I believe it is being multiplied so it would look like (4x+3) (2x^2+4x) which is what I have set up on my paper but the number with the variable that has an exponent with it is confusing to me and I don't know what to do with that exponent.

Answer 1

(f * g(x)) = (2x² + 4x)(4x + 3)

(f * g(x)) = 8x³ + 22x² + 12x

Answer 2

So (F * G)(X) is actually equal to F(G(X)), so if we were to substitute the equations into the expression, it would look a little something like this:

(F * G)(X) = F(G(X))

= 4(2x² + 4x) +3

= 8x² + 16x + 3