Plz help me solve the problem.

Problem 6. (15 points) (a) (5 points) Let f : (0, 00) > R be the function given by f(:r) = i, for every x G (O, 00). Prove that f is continuous at :r = 1 by using the 5-6 property. (b) (5 points) Let a, > 1. Prove that there exists a: E R such that 3:4 + a: + 1 = a. (c) (5 points) Let S be a nonempty set of real numbers and g : S > R be a function. Assume that g is uniformly continuous on S and |g(a:)| S 1, for every 3: G S. Prove that 92 is uniformly continuous on S