3. We study the function f defined below: f(x) = 124 if x is rational if x is irrational Prove that f is nowhere continuous except at x = 0. That is, you need to prove the following two statements. (1) (2 marks) f is continuous at r = 0. (2) (3 marks) f is not continuous at x = a for any a # 0. 4. Consider the function g(x) = 2-wx ifxsa if x > a Use the IVT (Intermediate Value Theorem) to justify that there exists a value of a which makes g continuous everywhere. 2