Question

F(x)=-4x+2 g(x)=6x+4

Fog , gof =?

Answer 1

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

(f · g) = (-4x + 2)(6x + 4)
(f · g) = -4x(6x + 4) + 2(6x + 4)
(f · g) = -4x(6x) - 4x(4) + 2(6x) + 2(4)
(f · g) = -24x² - 16x + 12x + 8
(f · g) = -24x - 4x + 8

(g · f) = (6x + 4)(-4x + 2)
(g · f) = 6x(-4x + 2) + 4(-4x + 2)
(g · f) = 6x(-4x) + 6x(2) + 4(-4x) + 4(2)
(g · f) = -24x² + 12x - 16x + 8
(g · f) = -24x² - 4x + 8

Answer 2

`f(g(x))=f(6x+4)\\f(6x+4)=4(6x+4)+2\\f(6x+4)=24x+16+2\\f(6x+4)=24x+18\\\\g(f(x))=g(4x+2)\\g(4x+2)=6(4x+2)+4\\g(4x+2)=24x+12+4\\g(4x+2)=24x+16`