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 )