Question

F(x)=3x+2

F(g(x)`)=7x+4/3
g(x)=?

Answer 1

f^-1(x) = (x-2)/3

Now, using the definition of an inverse function,
f^-1(f(g))=g
So,
(f(g)-2)/3 = g
((7x+4)/3-2)/3 = g
g(x) = (7x-2)/9

check:
f(g)=3g+2 = 3((7x-2)/9)+2 = (7x-2)/3+2 = (7x+4)/3