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Show That F(X) = G(X) For All X

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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