Question

Let f(x) = -4x - 2 and g(x) = 5x - 6. Find f⋅g and state its domain.

Answer 1

`(f*g)(x)=-20x^2+14x+12`

Domain: All Real Numbers.

Explanation:

Given the function f(x):

`f(x) = -4x - 2`

And the function g(x):

`g(x) = 5x - 6`

You need to multiply them. Then:

`(f*g)(x)=( -4x - 2)( 5x - 6)\\\\(f*g)(x)=-20x^2+24x-10x+12\\\\(f*g)(x)=-20x^2+14x+12`

Since we know that the domain is the set of all real values of the variable "x" that will give real values for the variable "y", the domain of
`(f*g)(x)=-20x^2+14x+12` is ALL REAL NUMBERS.

Answer 2

-20x^2 +14x+12

The domain of f*g is all real numbers

Explanation:

f(x) = -4x - 2

g(x) = 5x - 6.

f*g = (-4x-2) * (5x-6)

FOIL

first -4x*5x = -20x^2

outer -4x*-6 = 24x

inner -2*5x = -10x

last -2 *-6 = 12

Add them together

-20x^2 +24x-10x+12 = -20x^2 +14x+12

The domain of f is all real numbers, the domain of g is all real numbers

The domain of f*g is all real numbers