x+(1/x)=N+(1/N)
Nx^2+N=(N^2+1)x
Nx^2-(N^2+1)+N=0
x=(N^2+1)+/-sqrt[(N^2+1)^2-4N^2] /2N
x=(N^2+1)+/-sqrt[(N^2-1)^2] /2N
x=(N^2+1)+/-(N^2-1) /2N
x=N or N^2+1-(N^2-1) /2N
x=N or 1/N
Hence, f(N)=f(1/N). Since N<1, 1/N>1 and therefore lies in the domain x>=1.
=> f^(-1)[f(N)]=f^(-1)[f(1/N)]=1/N