Lebl-Basic-Analysis-I · Problem 3.2.10

Continuous Functions

Mathematics · continuous-functions

Problem

Let

f : \mathbb{R} \to \mathbb{R}

and

g : \mathbb{R} \to \mathbb{R}

be continuous functions. Suppose that

f(r) = g(r)

for all

r \in \mathbb{Q}

. Show that

f(x) = g(x)

for all

x \in \mathbb{R}