Well, it seems right to me...
f^{-1}(x) = c^n/x^n
f(x) = c/x^(1/n)
which gives,
f(f^{-1}(x)) = x = f^{-1}(f(x))
And, I am not using the complex roots of x^(1/n), which I stated in the Preliminaries section of the paper that we are only working with positive reals...
Thanks
Roupam