Note that f(1) = 6(1)+2 = 8. Next, evaluate g(x) at x=8: g(f(1)) = g(8) = 2(8) + 4/5, or 16 4/5.
I assume you mean
, and not
, since this doesn't satisfy the ODE.
Assume a second solution of the form
, where
is a function of
. Then


Substituting into the ODE gives







where we omit the second term because it's already accounted for by
.
There are a couple of answers, it could be 2+10 or 3+9