Question

Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f*g and state its domain.

-18x2 - 39x + 20; all real numbers except x = 1

-30x2 - 9x + 12; all real numbers

-18x2 - 39x + 20; all real numbers

-30x2 - 9x + 12; all real numbers except x = 4

Answer 1

1- getting f*g:
We are given that:
f (x) = -6x + 3
g (x) = 5x + 4
To get f*g, we will simply multiply the two functions as follows:
f (x) * g (x) = (-6x+3)(5x+4)
f (x) * g (x) = -30x² - 24x + 15x + 12
f (x) * g (x) = -30x² - 9x + 12

2- getting the domain:
The domain is all the values of x that can be used in the given equation.
In the equation calculated from part 1, we can note that all real numbers can be considered as the domain.

Hope this helps :)