fx3x24x4 gxx2 Domain needed for eachSolutionfx 3x2 4x 4 g

f(x)=3x²-4x-4, g(x)=x-2

Domain needed for each.

Solution

f(x) = 3x^2 - 4x - 4

g(x) = x - 2

f+g = f(x) + g(x) = 3x^2 - 4x - 4 + (x - 2) = 3x^2 - 4x - 4 + x - 2 = 3x^2 - 3x - 6

domain is all values of x (-infinity , + infinity )

f-g = f(x) - g(x) = 3x^2 - 4x - 4 - ( x - 2) = 3x^2 - 4x - 4 - x + 2 = 3x^2 - 5x - 2

domain is all values of x (-infinity , + infinity )

fg = f(x) * g(x) = (3x²-4x-4)* ( x-2) = 3x^3 - 4x^2 - 4x - 6x^2 + 8x + 8 = 3x^3 - 10x^2 + 4x + 8

domain is all values of x (-infinity , + infinity )

f/g = f(x) / g(x) = ( 3x^2 - 4x - 4) / ( x - 2) = ( x-2)(3x+2) / ( x-2) = 3x + 2

domain is all values of x (-infinity , + infinity )