How to rewrite g(x) in terms of f(x) when f(x)=1/x given g(x)=[4/(x-1)] 1?

Let y = f(x) = 1/x
Then, x = 1/y

If g(x) = [ 4/(x-1) ]
= [ 4/( 1/y - 1) ]
= [ 4/((1 - y)/y) ]
= [ 4y / (1 - y) ]
Therefore, since y = f(x).. so..

g(x) = [4 . f(x) / (1 - f(x)) ]