Problem 6.

Let f and g be continuous real-valued functions on R (meaning they are continuous

on all of R), such that f(r) = g(r) for every rational number r. Show that f(x) =

g(x) for all x.

Hint: Using the density of the rationals, show that if h is a continuous function on

[0, 1] such that h(r) = 0 for all rational numbers r, then h is 0.Math