math help please

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)= 2/3x-3, g(x) = 9x^2+2x+8, g(7) = 9(49)+2(7)+8 = 65(7)+8= 455+8=463

f(g(7)) = f(463) = 2/3(463)-3 = 2/1389 -3=(2-4167)/1389=- 4165/1389

g(f(4)) = g(2/12 -3) =g(-17/6)= 9(-17/6)^2 +2(-17/6)+ 8 = (-153-34)(-17/6) + 8= (-187)(-17/6)+8

= (187(17)+48)/6 = 3227/6

f(g(1/2) = f(9/4 +1+8) =f(45/4) = 2/3(45/4)-3 = 2/135/4 -3 = 8/135-3 = (8-405)/135 = -397/135

f(f(1/6) = f(2/3(1/6)-3) = f(2/1/2-3) = f(4-3)= f(1) = 2/3-3 = -7/3