please help! #16 is asking to find f(g(x)) and g(f(x)) using each pair of functions, #76 is asking to use the functions f(x)=2x^2 +1 and g(x)=3x+5 to evaluate or find the composite function

Question

#16. f(x)= 1/x-6 g(x)=7/x +6

#76. f(g(2))

Answer 1

f(x) = 2x^2 +1, g(x) =3x +5

f(g(x)) = f(3x+5) = 2(3x+5)^2 +1 = 2(9x^2 +30x +25) +1 = 18x^2 +60x +51

f(g(2)) = 18(2)^2+60(2)+51 = 72+120+51 =243

or f(g(2)) =f(3(2)+5) = f(11)= 2(11^) +1 =2(121)+1 =242+1 = 243

g(f(x)) = g(2x^2+1) = 3(2x^2+1)+5 = 6x^2 +3 +5 = 6x^2 +8

f(x)= 1/(x-6), g(x) =7/(x+6)

f(g(x)) = f(7/(x+6) = 1/((7/(x+6))-6) = 1/((7-6x-36)/(x+6)) = (x+6)/(-6x-29)= -(x+6)/(6x+29)

g(f(x)) = g(1/(x-6)) = 7/((1/(x-6)+6)) = 7/((6x-36+1)/(x-6)) =(7x-42)/(6x-35)