Question 805507
Use the given f and g to form their composition g(f(x)).  Note that the definition for g uses  variables, "a" and "b".  


{{{g(f(x))=a(3x-2)+b}}}
{{{3ax-2a+b}}}


This expression needs to be equal to how the composition was first defined in the given information.
{{{g(f(x))=9-6x=3ax-2a+b}}}
{{{9-6x=b-2a+3ax}}}
Look at the corresponding parts.
{{{9=b-2a}}} and {{{-6x=3ax}}}

.
The second equation here shows {{{-6=3a}}}, so {{{highlight(a=-2)}}}
Allowing you to solve for b, in {{{9=b-2a}}}, {{{9=b-2(-2)}}}, {{{9=b+4}}}, {{{highlight(b=5)}}}


NOW, you finish finding g(x).