If f(x)=g(g(x))-g(x) and g(x)=2x-1, find f(3).

Let's first find  g (g(x)) 

This is literally putting g(x)  into the x in  g(x)....so we have.... 

2 [ 2x - 1]  -  1    =    4x - 3

So  

g (g(x))  - g (x)   =

[ 4x - 3 ] - [ 2x  - 1 ]  =

2x  - 2    =  f(x)

So

f(3)   =  2(3) - 2     =   4