Functions

g(x) =  f ( f(x)  =

              1

_________________   =

 2   ( 1 / [2x - 5] ) - 5 

              1

_____________________   =

      2        -       5

______

  2x - 5

       2x  -   5

____________________    =

    2  -  5 [ 2x - 5]

      2x  - 5

____________

    27 - 10x

The x not in the domain  is

27 - 10x  = 0

27 = 10x

27 / 10  

I just read about pretty hard functions, hope I can solve it!!

$g(x)=f(f(x))=\frac{1}{2x-5}=\frac{1}{2(\frac{1}{2x-5})-5}=\frac{2x-5}{27-10x}$

Thus, the largest $x$ not in the domain of $g(x)$ is .$\boxed{\frac{27}{10}}.$