One-Way PermutationPRG

Problem 4. Suppose f : {0,1}n {0,1}n is a one-way permutation (i.e., it is a OWF and it is a permutation). Prove that G : {0,1}2n {0,1}2n+1 is a PRG, where G maps (x,r) {0,1}2n to (f(x),r,x,r) {0,1}2n+1 (hint: assume an efficient adversary can win the PRG game for G and design an efficient adversary who can win the inner product prediction game for f).

Remark. This proves that any OWF which is also a permutation can be used to construct a PRG. In fact, the extra assumption that f is a permutation is not needed, and the above construction (and analysis) can be extended to build a PRG starting from any OWF (though these changes are non-trivial)