Let \(f(x)=\frac{1}{2x-5}\). Find the largest \(x\) which is not in the domain of \(g(x)=f(f(x))\).
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