please help!! if you can’t do all please do one so i can figure out how to do the rest! i’m completely lost

Step-by-step explanation:

the domain is all values of x

(f ο g) (x) = f(g(x))

(g ο f) (x) = g(f(x))

1) f(x) = 6x+5, g(x) = 2x-4

(f ο g) (x) = f(g(x)) = f ( 2x-4) = 6* (2x-4) +5 = 12x -24 +5 = 12x -19

(g ο f) (x) = g(f(x)) = g( 6x +5) = 2*(6x+5) -4 = 12x +10-4 = 12x +6

x-can be anything

2) f(x)= 4x²-16, g(x) = √x+7

(f ο g) (x) = f(g(x)) = f(√x+7) = 4*(√x+7)² -16 = 4(x+7) -16 = 4x +28-16 = 4x +12

(g ο f) (x) = g(f(x))= g(4x²-16) = √4x²-16+7 = √4x²-9 = √(2x-3)(2x+3)

x-can be anything

3) f(x) = 5/(x-4), g(x) = 4x+4

(f ο g) (x) = f(g(x)) = f(4x+4) = 5/(4x+4-4) = 5/4x

(g ο f) (x) = g(f(x)) = g(5/(x-4)) =( 4*5/(x-4) ) +4 = (20/(x-4)) + 4(x-4)/(x-4)

= (20+4x-16) / (x-4) = 4x+4/x-4 = 4(x+1)/(x-4)

here the domain must exclude some values for x so you do not divide a fraction by a zero, x ≠0 for (fοg)(x) and x≠4 for (gοf)(x)

equal to

step-by-step explanation:

step-by-step explanation: