3. Suppose that the function f : R > R has the property that f(u + 'U) = u) + f(v) for all 'u,'u E R. (a) (2 points) Prove that if f(1) = m, then f(:c) = ms: for all rational 3:. (b) (4 points) Prove that if f : R > R is continuous, then there exists a constant m such that f(x) 2 ms: for all a: E R. (c) (4 points) Prove that if f is continuous at some 1:0 6 R, then there exists a. constant m such that f(:r) = mm for all a: E R