PLEASE HELP ME I'LL GIVE YOU THE REST OF MY POINTS!!! The 9th and 14th terms of an arithmetic sequence are 23 and 33, respectively. What is the 1st term?

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)