Math Help - I wanna prove if the composite are equal to each other

1. I wanna prove if the composite are equal to each other

Given f:{0,1}^n→{0,1}^n, deﬁne f′:{0,1}^(2n)→{0,1}^(2n) as follows: for x,r∈{0,1}^n deﬁne f′(x∘r):=f(x)∘r (where ∘ denotes concatenation). Prove that if f(⋅) is one way permutation then so is f′(⋅).

i don't understand f′(x∘r):=f(x)∘r how to decompose it in order to prove it

I tried proving it by using a composition of tow bijection, as a permutation is a sect of bijection function.

I am stuck on the proof, I dont know how to do the proof

2. Re: I wanna prove if the composite are equal to each other

Hey figo12.

Do you have a definition for r? (I'm a little rusty on permutations). Is r some kind of special mapping?