solve

BONUS Let f be a continuous function on R such that f(q) = 0 for all rational numbers q Q. Prove that f(x) = 0 for all x R. Hint: Let rr be an arbitrary irrational number. Recall Q is dense in R. This means there is a sequence of rational number q,, such that dn r. Now use sequential continuity to show f(r) = 0