Question

30 points if you answer this question and please show work !!

Answer 1

I don't know what is between f(x) and g(x), so (for now) there are two posible answers:

1. $f(x)g(x) = f(x)\cdot g(x)$ - function multiplication:

$f(x)g(x)=(2x-3)\cdot(3x+8)=2x\cdot3x+2x\cdot8-3\cdot3x-3\cdot8=\\\\=6x^2+16x-9x-24=\boxed{6x^2+7x-24}$

2. $f(x)g(x)=f(x)\circ g(x)$ - function composition:

$f(x)g(x) = f(x)\circ g(x) = f\big(g(x)\big)=2(3x+8)-3=2\cdot3x+2\cdot8-3=\\\\=6x+16-3=\boxed{6x+13}$