Math help don't understand it can someone please help me with it explain it and show me how to do it

Question

Function Composition Given the function f(x)=2/3x−3 and the function g(x)=9x^2+2x+8 determine each of the following.

Give your answer as an integer or a simplified fraction.

Evaluate f(g(7)) f(g(7))= 

 Evaluate g(f(4)) g(f(4))=

 Evaluate f(g(1/2)) f(g(1/2))=

 Evaluate f(f(1/6)) f(f(1/6))= 

Answer 1

f(x) = (2/3)x-3, g(x)= 9x^2+2x+8, g(7)= 9(7)(7)+2(7)+8 = 65(7)+8 = 455+8= 463

f(g(7)) = f(463) = (2/3)(463)-3 = 926/3- 3 = (926-9)/3 = 917/3

f(4) = (2/3)(4)-3 = 8/3-3 =8/3-9/3 =-1/3

g(f(4) =g(-1/3) = 9(-1/3)^2 +2(-1/3)+ 8 =1-2/3 +8 = 1/3+8 =25/3

g(1/2) = 9(1/2)^2+2(1/2)+8 = 9/4+1+8 = 9/4+9 = 45/4

f(g(1/2)= f(45/4) = (2/3)(45/4)-3 =15/2-3 = 9/2

f(1/6) = (2/3(1/6)-3= 1/9-3 = 1/9-27/9 =-26/9

f(f(1/6) = f(-26/9) = (2/3)(-26/9)-3 = -52/27-81/27=-133/27

UNLESS you meant f(x) = (2/(3x)) -3

then see the answer to the other time you earlier posted this same question

or if you really meant f(x)=2/(3x-3) you get different solutions

g(7)=9(7^2)+2(7)+8=463

f(g(7)) = f(463) =2/(3(463)-3) = 2/(1389-3) =2/1386= 1/693

f(4) = 2/9

g(f(4))=g(2/9)=9(2/9)^2 +2(2/9)+8 = 8/9+72/9 = 80/9

g(1/2) = 9(1/2)^2 +2(1/2)+8 = 9/4+9 =45/4

f(g(1/2))=f(45/4) =2/(135/4 -3)=2/123/4= 8/123

f(1/6) =2/-5/2=-4/5

f(f(1/6) = f(-4/5)=2/(3(-4/5)-3) = 2/(-12/5-15/5) = 2/-27/5= -10/27