please answer these questions for me and show each step

1. (5) Prove that f(x) = x3 is uniformly continuous on [2, 3]. 2. (5) Consider the function f(x) = x2. Find the inverse image of the open interval (a, b). Is it open? 3. (5) Prove that f(x) = x2 is uniformly continuous on [2, 3] in two ways. First use the definition directly to prove that it. Second, use a couple theorems to prove it. (This second proof should be no longer than two sentences.)