3. Suppose that the function f : R > R has the property that u + v) = u) + t!) for all 11,1) E R. (a) (2 points) Prove that if f(1) = m, then f(:r;) = 111.1: for all rational 3:. (b) (4 points) Prove that if f : R > R is continuous, then there exists a constant m such that f (3:) = mm for all a: E R. (c) (4 points) Prove that if f is continuous at some :80 E R, then there exists a constant m such that f(a:) = mm for all a: E R