Question

Let f(x) = -2x + 7 and g(x) = -6x + 3. Find f x g and state its domain.

a. 12x^2 - 48x + 21; all real numbers except x = 1
b. 12x^2 - 48x + 21; all real numbers
c.-14x^2 + 36x - 18; all real numbers
d.-14x^2 + 36x - 18; all real numbers except x = 7

Answer 1

b)
`12x^2-48x+21` ; all real numbers

Explanation:

f and g are polynomials and polynomials have domain all real numbers.

This is because when you input any number there will always be a existing output. There are no restrictions on what you can plug into a polynomial.

So the answer is either b or c.

`(f * g)(x)=f(x) * g(x)`

`(f * g)(x)=(-2x+7) * (-6x+3)`

`f * g)(x)=(-2x+7)(-6x+3)`

Let's use foil!

First:
`-2x(-6x)=12x^2`

Outer:
`-2x(3)=-6x`

Inner:
`7(-6x)=-42x`

Last:
`7(3)=21`

-----------------------------Add like terms:

`12x^2-48x+21`

The answer is b.