Question

The domain for f(x)=2x^2+x-3 and g(x) = x-1. find f(x) * g(x)

Answer 1

Hello there. To solve this question, we'll have to remember some properties about domain of functions and the product between two polynomial functions.

Given the functions

`\begin{gathered} f(x)=2x^2+x-3 \\ \\ g(x)=x-1 \\ \end{gathered}`

and knowing that

`Dom(f)=Dom(g)=\mathbb{R}`

We want to determine the expression for

`f(x)\cdot g(x)`

For this, we plug the functions

`(2x^2+x-3)\cdot(x-1)`

The domain is important to know when it asks you to determine the domain of the new expression, but in this case, to take the product, we can simply apply the FOIL

`\begin{gathered} 2x^2\cdot x+2x^2\cdot(-1)+x\cdot x+x\cdot(-1)-3\cdot x-3\cdot(-1) \\ \\ 2x^3-2x^2+x^2-x-3x+3 \\ \\ 2x^3-x^2-4x+3 \end{gathered}`

This is the answer to this question and it is contained in the second option.