Find the functions f g g f f f and g g and their domains fx

Find the functions f g, g f, f f, and g g and their domains. f(x) = 4x + 5, g(x) = 2x - 1 (f g)(x) = Domain: (-infinity, 0) (0, infinity) (-infinity, -5) (-5, infinity) (-infinity, -5] [-5, infinity) (-infinity, infinity) (g f)(x) = Domain: (-infinity, -5) [5, infinity) (-infinity, infinity) (-infinity, 0) (0, infinity] (-infinity, -5) (-5, infinity) 9f f)(x) = (-infinity, -5] (-infinity, infinity) [-5, infinity) (-infinity, 0) (0, infinity) (-infinity, -5) (-5, infinity)

Solution

f(x)= 4x+5 and g(x)=2x-1

(fog)(x)= f(g(x))= f(2x-1)

                           = 4(2x-1) + 5= 8x+1

Therefore (fog)(x)= 2x+4

(gof)(x)= g(f(x))= g(4x+5)

                         = 2(4x+5) - 1= 8x + 9

Therefore gof(x)= 8x+9

(fof)(x)= f(f(x))= f(4x+5)

                       = 4(4x+5) + 5= 16x + 25

therefore (fof)(x)= 16x+ 25

(gog)(x)= g(g(x))= g(2x-1)

                            = 2(2x-1) -1= 4x-3

Therefore (gog)(x)= 4x-3