I've been working on this problem for my analysis class for a while now, and I don't have any idea where to go. Any help at all would be greatly appreciated. Thanks!

Suppose p is an odd prime. Define the set P = {x in Q_p: |x|_p < 1}, that is, the p-adic numbers that have p-adic absolute value less than 1. Define U_1 = P + 1. Prove that the function f(x) = x^2 from U_1 to U_1 is a bijection.