Let f:R --> R be a function that satisfies f(x+y)=f(x)+f(y) for all x, y as an element in R.

(a) Suppose that f is continuous at some point c. Prove that f is continuous on R.

(b) Suppose that f is continuous on R and that f(1)=k. Prove that f(x) = kx for all x as an element in R.