Given the functions, f ( x ) = x2 + x - 5 and g ( x ) = 4 x2 - 2 x + 1, perform the indicated operation. When applicable, state the domain restriction. ( f - g )( x )

(f-g)(x)  =  - 3 x² + 3 x -6

Step-by-step explanation:

Explanation:-

Given function f(x) = x² + x - 5

                      g(x) = 4 x² - 2 x + 1

(f-g)(x)   =  f(x) - g(x)

            =  x² + x - 5 - (4 x² - 2 x + 1)

            = x² - 4 x² + x + 2 x - 5 -1

            =  - 3 x² + 3 x -6

(f-g)(x)  =  - 3 x² + 3 x -6

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15